To a remarkable extent, our understanding of the natural world is built from a small set of very deep ideas. I’ll try to give some sense for the nature of these ideas, for their power and scope. I will also try to explain what we mean by “understanding” in several different contexts, and why these successes give us (measured) confidence that more complex problems may yet yield to our search for understanding. Finally, I’ll say a few words about the cultural gaps that separate scientists who have mastery of these theoretical ideas from other scientists, from the generally educated public, and from the polity as a whole. It is not too much to claim that our future quality of life will depend, crucially, on our ability to bridge these gaps by teaching.