'The Lucan problem has all at once become a burning one, ' says a famous German scholar, Professor Ernst Kasemann, in a recent book. Few English readers, it is fair to say, so much as know that there is a problem. This problem involves not only renewed discussions of the life of Jesus, but also questions about the apostolic Church--its gospel and preaching, its common life and ministry. This lecture first offers a short account of some of the most important recent contributions to the understanding of Luke's work, and then considers some of the problems afresh. What made Luke a historian, and led him--alone, so far as we know, among his contemporaries--to write the story of Christianity from the birth of Jesus to Paul's mission to Rome? How was his work affected by the example of older historians? What was his attitude to the theological problems of his day? What did he set out to achieve in his two volumes? What lessons may the twentieth-century Church learn from his work? These are among the questions raised by this lecture.