We are fortunate to live at a time when questions about the origin and future of the universe are becoming accessible to scientific inquiry, primarily through observational advances but also through the development of new theoretical ideas. One popular picture is that the very early universe underwent an extraordinary burst of exponential expansion, known as cosmic inflation. An alternative is that the big bang we see in our past is only the latest in an infinite series of cosmic cycles of expansion and contraction. In this colloquium, I will compare and critique these ideas and explain why, in my view, neither yet convincingly explains the astonishing simplicity revealed by observations of the universe on the largest visible scales.