A major goal of artificial intelligence (AI) is to create an agent capable of acquiring a general understanding of the world. Such an agent would require the ability to continually accumulate and build upon its knowledge as it encounters new experiences. Lifelong or continual learning addresses this setting, whereby an agent faces a continual stream of problems and must strive to capture the knowledge necessary for solving each new task it encounters. If the agent is capable of accumulating knowledge in some form of compositional representation, it could then selectively reuse and combine relevant pieces of knowledge to construct novel solutions. Despite the intuitive appeal of this simple idea, the literatures on lifelong learning and compositional learning have proceeded largely separately. In an effort to promote developments that bridge between the two fields, this article surveys their respective research landscapes and discusses existing and future connections between them.