Cognitive control allows us to think and behave flexibly based on our context and goals. At the heart of theories of cognitive control is a control representation that enables the same input to produce different outputs contingent on contextual factors. In this review, we focus on an important property of the control representation’s neural code: its representational dimensionality. Dimensionality of a neural representation balances a basic separability/generalizability trade-off in neural computation. We will discuss the implications of this trade-off for cognitive control. We will then briefly review current neuroscience findings regarding the dimensionality of control representations in the brain, particularly the prefrontal cortex. We conclude by highlighting open questions and crucial directions for future research.