Function allocation is the design decision which assigns work functions to all agents in a team, both human and automated. Efforts to guide function allocation systematically has been studied in many fields such as engineering, human factors, team and organization design, management science, and cognitive systems engineering. Each field focuses on certain aspects of function allocation, but not all; thus, an independent discussion of each does not address all necessary issues with function allocation. Four distinctive perspectives emerged from a review of these fields: technology-centered, human-centered, team-oriented, and work-oriented. Each perspective focuses on different aspects of function allocation: capabilities and characteristics of agents (automation or human), team structure and processes, and work structure and the work environment. Together, these perspectives identify the following eight issues with function allocation: 1)Workload, 2)Incoherency in function allocations, 3)Mismatches between responsibility and authority, 4)Interruptive automation, 5)Automation boundary conditions, 6)Function allocation preventing human adaptation to context, 7)Function allocation destabilizing the humans' work environment, and 8)Mission Performance. Addressing these issues systematically requires formal models and simulations that include all necessary aspects of human-automation function allocation: the work environment, the dynamics inherent to the work, agents, and relationships among them. Also, addressing these issues requires not only a (static) model, but also a (dynamic) simulation that captures temporal aspects of work such as the timing of actions and their impact on the agent's work. Therefore, with properly modeled work as described by the work environment, the dynamics inherent to the work, agents, and relationships among them, a modeling framework developed by this thesis, which includes static work models and dynamic simulation, can capture the issues with function allocation. Then, based on the eight issues, eight types of metrics are established. The purpose of these metrics is to assess the extent to which each issue exists with a given function allocation. Specifically, the eight types of metrics assess workload, coherency of a function allocation, mismatches between responsibility and authority, interruptive automation, automation boundary conditions, human adaptation to context, stability of the human's work environment, and mission performance. Finally, to validate the modeling framework and the metrics, a case study was conducted modeling four different function allocations between a pilot and flight deck automation during the arrival and approach phases of flight. A range of pilot cognitive control modes and maximum human taskload limits were also included in the model. The metrics were assessed for these four function allocations and analyzed to validate capability of the metrics to identify important issues in given function allocations. In addition, the design insights provided by the metrics are highlighted This thesis concludes with a discussion of mechanisms for further validating the modeling framework and function allocation metrics developed here, and highlights where these developments can be applied in research and in the design of function allocations in complex work environments such as aviation operations.