The recognition of teams as complex dynamic systems was a hallmark and among the earliest considerations of research on team functioning. However, the popularization of conceptual heuristics such as the input-process-outcome (IPO) framework and the accessibility of methodological, analytical, and meta-theoretical principles from multilevel theory (MLT) have resulted in a disconnect between contemporary theory and empirical research on teams and this foundational perspective. Thus, the primary motivation for the present paper is to facilitate and stimulate future research on team phenomena that embraces systems thinking. To do so, we describe key concepts, terminology, and ideas from specific branches of the systems sciences—namely open systems theory, dynamical systems, and agent-based systems—that have direct relevance for researching team phenomena as complex systems. Additionally, a comparison between two example models of team performance that are rooted in an IPO+MLT versus a systems-oriented perspective is offered to highlight the difference in foci, applications, and inferences these approaches offer. The paper concludes with a summary of key advantages as well as potential obstacles for reintroducing systems-thinking back into team science.