We discuss aspects of our knowledge of incompressible, wall-bounded turbulent flows in an attempt to identify the key issues and challenges. The emphasis is on the behavior at high Reynolds numbers, and the discussion is directed to constant-pressure boundary layers as well as to pipe and channel flows. Recent advances, spurred by a series of international workshops and experimental studies, challenge current textbook orthodoxy and it therefore appeared useful to present them in this form. We have included alternative perspectives where appropriate. Our account focuses on the mean velocity distribution, fluctuations, as well as a hierarchy of turbulence structures. Beyond posing the questions believed to be important, we also identify avenues of research that may provide answers to these questions. We believe that these views will contribute to the improved understanding of wall-bounded turbulence based on first principles, and thus advance our ability to model, compute, and predict its behavior.