In recent years, analytics has started to revolutionize the game of basketball: quantitative analyses of the game inform team strategy, management of player health and fitness, and how teams draft, sign, and trade players. In this review, we focus on methods for quantifying and characterizing basketball gameplay. At the team level, we discuss methods for characterizing team strategy and performance, while at the player level, we take a deep look into a myriad of tools for player evaluation. This includes metrics for overall player value, defensive ability, and shot modeling, and methods for understanding performance over multiple seasons via player production curves. We conclude with a discussion on the future of basketball analytics, and in particular highlight the need for causal inference in sports.