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In this chapter, entity refers to a person, group of people or organization whereas competencies refer to the knowledge, skills, abilities, attitudes, traits, and capabilities that define what an entity knows and can accomplish. The purpose of this chapter is to survey models for determining whether (or to what extent) an entity E has a set of competencies in a competency framework F related to a job, task, or domain. We call this the state of E with respect to F. In our formulation, the state at a given time t is defined by the values of functions (see Section 2) that can be estimated from data. Our goal is to present a variety of mathematical models, called state models, for computing this state. This state can play a role in predicting whether E will successfully perform a task and in determining how to best train or teach a competency. This chapter focuses only on mathematical models for computing competence.