Learning, development, and response to instruction often involve changes in the strategies that learners use to solve problems. In this chapter, our focus is on mathematical problem solving in both children and adults. We offer a selective review of research on three classes of factors that may influence processes of strategy change in mathematical problem solving: contextual factors, individual factors, and metacognitive factors. "Contextual factors" involve information that learners encounter in the learning context, such as feedback about prior strategies and examples of alternative strategies. "Individual factors" involve the abilities, dispositions, and knowledge that learners bring to the learning context. "Metacognitive factors" involve knowledge "about" strategies and factors that affect the application of strategies--including perceptions of problem difficulty, confidence in the strategies one already knows, and judgments about the qualities of alternative strategies. These factors operate both independently and in combination to influence learners' behavior. Therefore, we argue that scientific progress in understanding strategy change will require comprehensive conceptual models that specify how different factors come together to explain behavior. We discuss several such models, including vulnerability-trigger models, cumulative risk models, and dynamic systems models. Research guided by such models will contribute to greater progress in understanding processes of strategy use and strategy change. [This paper was published in "Advances in Child Development and Behavior" v56 p227-256 2019.]