If the whole universe obeys the laws of quantum mechanics then the universe has a quantum state — a wave function of the universe. This state specifies how the universe started at the big bang. It provides quantum probabilities for everything that happened since. A theory of this wave function is a necessary part of any "theory of everything". We will discuss what the wave function predicts and what it does not predict using the no-boundary wave function of the universe as an example. Approximate homogeneity of the universe is predicted on very large distance scales. But the wave function also predicts the fluctuations away from homogeneity that we see in the cosmic background radiation near the time of the big bang and in the large scale distribution of the galaxies today. We will conclude with a discussion of the evolution of complexity in the universe and the epochs in its history most favorable to life.