Predictions in the social world generally influence the target of prediction, a phenomenon known as performativity. Self-fulfilling and self-negating predictions are examples of performativity. Of fundamental importance to economics, finance, and the social sciences, the notion has been absent from the development of machine learning that builds on the static perspective of pattern recognition. In machine learning applications, however, performativity often surfaces as distribution shift. A predictive model deployed on a digital platform, for example, influences behavior and thereby changes the data-generating distribution. We discuss the recently founded area of performative prediction that provides a definition and conceptual framework to study performativity in machine learning. A key element of performative prediction is a natural equilibrium notion that gives rise to new optimization challenges. What emerges is a distinction between learning and steering, two mechanisms at play in performative prediction. Steering is in turn intimately related to questions of power in digital markets. The notion of performative power that we review gives an answer to the question how much a platform can steer participants through its predictions. We end on a discussion of future directions, such as the role that performativity plays in contesting algorithmic systems.