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Researchers in human–robot collaboration have extensively studied methods for inferring human intentions and predicting their actions, as this is an important precursor for robots to provide useful assistance. We review contemporary methods for intention inference and human activity prediction. Our survey finds that intentions and goals are often inferred via Bayesian posterior estimation and Markov decision processes that model internal human states as unobserved variables or represent both agents in a shared probabilistic framework. An alternative approach is to use neural networks and other supervised learning approaches to directly map observable outcomes to intentions and to make predictions about future human activity based on past observations. That said, due to the complexity of human intentions, existing work usually reasons about limited domains, makes unrealistic simplifications about intentions, and is mostly constrained to short-term predictions. This state of the art provides opportunity for future research that could include more nuanced models of intents, reason over longer horizons, and account for the human tendency to adapt.