A common criticism of Karl Barth is that he does not sufficiently address the problems of the modern person. Theologians like Rudolf Bultmann, Paul Tillich, and even Dietrich Bonhoeffer concerned themselves with the question of how we can proclaim the gospel in an age that cares less and less about God, the church, or theology. They searched in vain for an answer to this in Barth's works--or, rather, they were disappointed with the answers they found.
I, however, find Barth's approach to this issue quite compelling, and so I'd like to explain what it is, and why I like it. (Barth enthusiasts will want to pay attention to the endnotes.)
Barth makes special note of this problem in The Humanity of God, published in 1956. Here, he responds to Bonhoeffer's criticism of him. Bonhoeffer had written in his letters from prison that Barth did not provide any guidance on how to interpret theological concepts for a world come of age, for nonreligious people, and so leaves the world to its own devices, ending up with a "positivism of revelation." Modern people don't understand the need for biblical proclamation and theological exposition, and Bonhoeffer thought theologians should take this seriously instead of going on their merry way.
In response, Barth says that the so-called "world come of age" only imagines itself as such, but really is not as adult as it thinks it is. He also says Christians are not outsiders to this world come of age. We are all modern people, and so whenever we proclaim the gospel, we proclaim it as modern people. One of Barth's students, while discussing certain biblical material in class, asked Barth, "But how can you make that understandable to modern man?" Barth responded, "You're a modern man. Do you understand it?"
Barth's point is that we do not need to act like we are aliens from another planet visiting earth trying to make ourselves clear. If we can groove with Christianity, that must mean others can as well, without special help from "nonreligious interpretation."
Nonreligious interpretation, for Barth, can all-too-easily lead to compromising the Word of God for the sake of the world, and so Barth wants to err on the side of proclaiming the Word of God with the language we receive from Scripture and, secondarily, from the history of the church's proclamation.
Finally, Barth appeals to the inherent strangeness in the gospel message, making the point that the gospel will not measure up to the modern person's standard of comprehensibility because it is by nature an other Word to our human words.
That said, Barth incites us to make sure it is wonderfully strange, as it is a message of God's eternal love for the world. We will be heard by the world if we stay true to the Word of God in our proclamation, because the Word of God has genuine power--indeed, it has the power of God.
In the same year, Barth published volume IV.1 of his Church Dogmatics. Here, Barth extends his criticism of the modern human being. What might seem like adulthood is really a brazen claim to privilege and lordship, when people, in truth, are utterly dependent on God and are lowly creatures. The "coming of age" is really a transvaluation of God’s order. Barth goes so far as to compare the modern coming of age to Adam and Eve succumbing to the devil in the Fall.
However, Barth does not use this as an excuse to ignore unbelievers. On the contrary, he recognized the need for the church to be there for others and to be Christ’s presence to and for the world. In CD IV.2, he says, "There can be no divine revelation without a human ministry of witness." Human ministry is the love of neighbors which reflects God's love for us. Neglecting this aspect of the church’s task is neglecting the church’s task entirely.
Humans cannot love others and minister to others if they ignore their concerns and questions. This was at the heart of Bonhoeffer's critique of Barth. He essentially believed that Barth was doing too much highly concentrated theological explication and not enough interpretation of theological concepts for a nonreligious age. “The church is church only when it is there for others,” Bonhoeffer said.
But Barth thought ministry of the Word can be done for a nonreligious age if theological explication is done properly, and on its own terms. He might say that the most compelling interpretation of theological concepts is an accurate explication of them.
Barth did also say that a little bit of language "from the street, the newspaper, literature, and, if one is ambitious, from the philosopher" may be necessary for the purposes of communication, but ultimately he thought we should not try to dumb down the strangeness of the Word, for it is no stranger today than it was in past ages.
In a BBC interview, Vernon Sproxton asked him, “Do you think it is possible for modern man to hear the word of God clearly in the Bible?” Barth answered, “It is not easier and it is not more difficult for modern man, because for all men God is a stranger and God can only be heard and understood insofar as He Himself speaks to him. Now He speaks, but there will be a discontinuity on the side of man, not on the side of God, but on the side of man; and insofar it is always an event, if men understand Him. This event may happen in modern times as it happened in old times. I don't see a difference.”
As a Barthian theologian, I struggle with this point. On the one hand I am personally often at a loss for words when confronted with the task of explaining my theology or Barth’s theology to an unbeliever, or even to a lay Christian. When people ask me, “Why do you believe in God?” or “Why are you a Christian?” or “Who’s this Barth guy? What’s his deal?” I usually struggle to find a way to explain the subject without having them think I mean something I do not mean.
On the other hand, I do resist the tendency to think that it was easier for Paul or for Martin Luther to believe that Jesus was raised from the dead and that “the sufferings of this present time are not worth comparing with the glory about to be revealed to us” (Rom. 8:18), than it is for us today. Was this really easier to believe while Christians were being persecuted in Rome? Or in the plague-stricken world of medieval Europe? Is the modern person really that special?
And is there not something to say for Barth’s critique of modernity? Should we be surprised, for example, that the age of human autonomy and "adulthood" so easily became the age of the Anthropocene?
I think Barth was right to demean the importance of modern questions, which are often asked as if their significance and ultimacy are self-evident. He was also right to criticize human self-assertion. Are Hitler and Stalin not also products of the "world come of age"?
Ultimately, I think the best thing that can be said on this issue is something both Bonhoeffer and Barth affirmed. That is, Christians must be there for others, serve others, and reflect the love of God to others. I think it will be in this activity that we will find a way to communicate the gospel to our secular friends and family without compromising the strangeness of it, but also without practicing a "positivism of revelation" and merely expecting them to get on board with theological concepts they might understand as outdated, or might not understand at all, or even might have bad associations with (e.g., fatherhood, lordship, obedience, etc.).
How do we interpret theological concepts for the modern person? We can only answer this by being with and being for modern people.
 Here is the full passage I'll be drawing from: "We cannot at all reckon in a serious way with real "outsiders," with a "world come of age," but only with a world which regards itself as of age (and proves daily that it is precisely not that). The so-called "outsiders" are really only "insiders" who have not yet understood and apprehended themselves as such. On the other hand, even the most persuaded Christian, in the final analysis, must and will recognize himself ever and again as an "outsider." So there must then be no particular language for insiders and outsiders. Both are contemporary men-of-the-world—all of us are. A little “non-religious” language from the street, the newspaper, literature, and, if one is ambitious, from the philosopher may thus, for the sake of communication, occasionally indeed be in order. However, we should not become particularly concerned about this. A little of the language of Canaan, a little "revelation-positivism," can also be a good thing in addressing us all and … will often, though not always, be still better understood even by the oddest strangers. That is better than feeling compelled to approach them … with some sort of gibberish, which, for the moment, is modern. What we have to say to them—and first to ourselves—is a strange piece of news in any case. Let us see to it that it really is the great piece of news—the message of eternal love of God directed to us men as we at all times were, are, and shall be. Then we shall certainly be very well understood by them, whatever they may or may not do with it. He whose heart is really with God and therefore really with men may have faith that the Word of God, to which he seeks to bear witness, will not return unto Him void." Karl Barth, The Humanity of God, trans. John Newton Thomas and Thomas Wieser (Louisville: Westminster John Knox Press, 1960), 58-59.
 Testimony from William Rader, a student of Barth’s at the University of Basel from 1960-61: http://barth.ptsem.edu/people/former_student/william-rader.
 In CD IV.3, published in 1959, Barth strengthens this point. He says, “all religious language is also and indeed primarily non-religious,” so that anything “the Christian community has to say, it can say only after worldly fashion, each term being worldly at root and each expression worldly in its original meaning.” There is thus no need to “escape being secular,” nor to “try to escape from a sacred sphere of language … into a supposedly more secular realm in order to achieve perhaps a better or easier understanding. … It can speak only in secular terms.” The issue of nonreligious interpretation is thus resolved for Barth. There is no such thing as “nonreligious” language, for all language is always already conditioned and determined by its surroundings. If I can understand it, you can understand it. If he can understand it, we can understand. See Karl Barth, Church Dogmatics, Vol. IV: The Doctrine of Reconciliation, Part 3.2. eds. G. W. Bromily and T. F. Torrance, trans. G. W. Bromily (New York: T&T Clark, 1961 [repr. Peabody: Hendrickson Publishers, 2010]), 735, 736.
This is consistent with a position he laid out in CD I.1: "It is not the case that God has something and somewhere a Church with its preaching and sacraments—but history and society stand apart from all this, unaffected, sovereign, following their own laws, and the Church must come as it were from outside, from a God who has remained alien to this cosmos, to represent and champion its cause, or the cause of its God, to this cosmos by attack or defence. It is not at all true that the Church is outside with God and the world is inside without God. … But in this case the world cannot be held to its ungodliness by the Church; it cannot be taken seriously in its ungodliness. … Not in the light of nature but in the light of grace, there is no self-enclosed and protected secular sphere, but only one which is called in question by God’s Word, by the Gospel, by God’s claim, judgment, and blessing, and which is only provisionally and restrictedly abandoned to its own legalism and its own gods. … The world, then, cannot evolve into agreement with God’s Word on its own initiative nor can the Church achieve this by its work in and on the world." Karl Barth, Church Dogmatics, Vol. I: The Doctrine of the Word of God, Part 1, 2nd ed., eds. G. W. Bromily and T. F. Torrance, trans. G. W. Bromily (New York: T&T Clark, 1975 [Peabody, Mass.: Hendrickson Publishers, 2010]), 154-155.
 Similarly, he says in volume I.1 of the Church Dogmatics, "The church ... will have something to say to the world and will be taken seriously by the world. … Precisely here it should not be forgotten that the Word of God is and remains the speech of God, and its power … is thus the power of truth. The face that the truth … is also power is something we can state without reservation in the present context.” Barth, CD I.1, 156.
 Karl Barth, Church Dogmatics, Vol. IV: The Doctrine of Reconciliation, Part 1, eds. G. W. Bromily and T. F. Torrance, trans. G. W. Bromily (New York: T&T Clark, 1956 [repr. Peabody: Hendrickson Publishers, 2010]).
Here are the relevant passages: “The emancipation of man,” he says, “his exaltation from servant to lord, seems to be nothing other than his inevitable and ordained coming of age, and to that extent again the legitimate fulfilment of his true human development.” However, things are not always as they may seem, and we must never forget that, “Evil always takes good care not to show itself as such. It always cloaks itself, hiding under the garment not only of innocence but of an exalted virtue" (p.434, emphasis added). He describes the Fall as the human coming of age: “the serpent does not need to say it but man can and will deduce it for himself—it is time for man to be enlightened and to come of age” (p.435). “Man may call the thing his true development,” he says, but “it still disrupts and deforms … the basic relationship of all created being: the relationship of Creator and creature, and of God and man in particular” (p.436). All of this crescendos in a decisive No to the human being’s supposed adulthood: "In spite of all the movement in his historical forms and activities, man himself is not progressive. In respect of his capacity, or incapacity, to live as homo sapiens, to make his being and his being together tolerable and stable, he is remarkably stationary, his actions and reactions being unfortunately only too similar to those of an unreasoning bullock plodding around a capstan. His pride is his hindrance, and it is one of the imaginations of his pride that one day he will achieve this modest control of his life. … But the really outstanding thing beyond and in the antitheses is the all-conquering monotony—the monotony of the pride in which man has obviously always lived to his own detriment and to that of his neighbour. … The man of pride can only live to his own and his neighbour’s detriment" (p.507).
 Karl Barth, Church Dogmatics, Vol. IV: The Doctrine of Reconciliation, Part 2, eds. G. W. Bromily and T. F. Torrance, trans. G. W. Bromily (New York: T&T Clark, 1958 [repr. Peabody: Hendrickson Publishers, 2010]), 818, emphasis added.
 Ibid., 817.
 Dietrich Bonhoeffer, Letters and Papers from Prison, in The Bonhoeffer Reader, eds. Clifford J. Green and Michael P. DeJonge (Minneapolis: Fortress Press, 2013), 766.
 Barth, The Humanity of God, 59. He makes a similar point in CD I.1: "The concrete encounter of God and man to-day … must find a counterpart in the human event of proclamation, i.e., the person called must be ready to make the promise given to the Church intelligible in his own words to the men of his own time." Barth, CD I.1, 59.
 Quoted in David W. Congdon, The Mission of Demythologizing: Rudolf Bultmann’s Dialectical Theology (Minneapolis: Fortress Press, 2015), 215 n.449.