Although teams are considered to be the building blocks of modern organizational designs and numerous theoretical models, and narrative and meta-analytic reviews of the literature exist, there is a lack of coherence, integration, and understanding of how team composition effects relate to important team outcomes. Accordingly we have five primary goals for this article. First, we categorize team composition models into four types and highlight theory and research associated with each one. Second, we offer an integrative framework that represents members’ attributes as simultaneously contributing variance to each of the four model types. Third, we overlay temporal considerations that suggest different team compositional mixes will be more or less salient at different periods of performance episodes or stages of team development. Fourth, we integrate membership dynamics into our model. And fifth, we advance an integrative optimization algorithm that incorporates implications from all for the four previous approaches, as well as temporal dynamics and membership change. In so doing, we provide a synthesis of previous work and theories and outline a research agenda for both research and practice.