As expensive, high-throughput experiments become routine, it is increasingly important to make efficient use of limited experimental resources. Unfortunately, in complex settings human intuition may not be up to the task of making suitable choices for the many design parameters that enter into intricate experiments. Bayesian optimal experimental design (OED) is a principled information-theoretic framework for automating certain aspects of experimental design. What makes OED particularly attractive is that it can enable adaptive experiments in which data from previous rounds informs the experimental design used in subsequent rounds. We give an introduction to the principles that underlie OED and show how recent advances in black-box variational inference make OED suitable for practical use.