Martin Rees discusses his early interest in natural phenomena; early reading in science; education at Cambridge; graduate work at Cambridge; influence of Dennis Sciama; work with Sciama on the steady state theory; Sciama's attitutde toward science; attitude of the Cambridge community toward the results of Martin Ryle on radio counts and challenges to the steady state model; early thinking on the horizon problem; Misner's work on the horizon problem; attitude toward the horizon problem and the role of quantum gravity; relationship of flatness problem to horizon problem; attitude toward the flatness problem; early history of inflationary ideas of Starobinsky and Englert; initial reaction to the inflationary universe model; importance of nonconservation of baryons to inflationary theories; reaction to de Lapparant, Geller, and Huchra's work on large-scale inhomogeneities; history of research on inhomogeneities in the universe; early work by Russians on the pancake model of galaxy formation; new cosmological problems that can be addressed in terms of physics rather than in terms of initial conditions: photon-to-baryon ratio, inflation, origin of density fluctuations; prematurity of cosmological questions; importance of evidence for dark matter; the success of the standard big bang model in surviving observational tests; relationship between theory and observation in cosmology; importance of understanding galactic evolution; outstanding problems in cosmology: initial conditions, origins of fluctuations, galaxy formation; question of whether the universe is inherently unique; ideal design of the universe; desire for unending complexities in the laws of nature; question of whether the universe has a point.