Cognitive scientists and neuroscientists are increasingly deploying computational models to develop testable theories of psychological functions and make quantitative predictions about cognition, brain activity and behaviour. Computational models are used to explain target phenomena such as experimental effects, individual and/or population differences. They do so by relating these phenomena to the underlying components of the model that map onto distinct cognitive mechanisms. These components make up a ``cognitive state space'', where different positions correspond to different cognitive states that produce variation in behaviour. We examine the rationale and practice of such model-based inferences and argue that model-based explanations typically miss a key ingredient: they fail to explain why and how agents occupy specific positions in this space. A critical insight is that the agent's position in the state space is not fixed, but that the behaviour they produce is the result of a trajectory. Therefore, we discuss (i) the constraints that limit movement in the state space, (ii) the reasons for moving around at all (i.e. agents' objectives); and (iii) the information and cognitive mechanisms that guide these movements. We review existing research practices, from experimental design to the model-based analysis of data, and discuss how these practices can (and should) be improved to capture the agent's dynamic trajectory in the state space. In so doing, we stand to gain better and more complete explanations of the variation in cognition and behaviour over time, between different environmental conditions and between different populations or individuals.