In the last several years, there has been significant theoretical progress on understanding the distributions of ranks and Selmer groups of elliptic curves over $\mathbb{Q}$, led by work of Bhargava and Shankar. In this talk, we will survey these results and the main ideas behind them, as well as discuss generalizations and applications. We will compare the expected behavior with data from a recent database of elliptic curves over $\mathbb{Q}$ ordered by height (joint work with Balakrishnan, Kaplan, Spicer, Stein, and Weigandt).