Converging evidence from psychology, human factors, management and organizational science, and other related fields suggests that humans working in teams employ shared mental models to represent and use pertinent information about the task, the equipment, the team members, and their roles. In particular, shared mental models are used to interact efficiently with other team members and to track progress in terms of goals, subgoals, achieved and planned states, as well as other team-related factors. Although much of the literature on shared mental models has focused on quantifying the success of teams that can use them effectively, there is little work on the types of data structures and processes that operate on them, which are required to operationalize shared mental models. This paper proposes the first comprehensive formal and computational framework based on results from human teams that can be used to implement shared mental models for artificial virtual and robotic agents. The formal portion of the framework specifies the necessary data structures and representations, whereas the computational framework specifies the necessary computational processes and their interactions to build, update, and maintain shared mental models.