Wilful movement requires neural control. Commonly, neural computations are thought to generate motor commands that bring the musculoskeletal system — that is, the plant — from its current physical state into a desired physical state. The current state can be estimated from past motor commands and from sensory information. Modelling movement on the basis of this concept of plant control strives to explain behaviour by identifying the computational principles for control signals that can reproduce the observed features of movements. From an alternative perspective, movements emerge in a dynamically coupled agent–environment system from the pursuit of subjective perceptual goals. Modelling movement on the basis of this concept of perceptual control aims to identify the controlled percepts and their coupling rules that can give rise to the observed characteristics of behaviour. In this Perspective, we discuss a broad spectrum of approaches to modelling human motor control and their notions of control signals, internal models, handling of sensory feedback delays and learning. We focus on the influence that the plant control and the perceptual control perspective may have on decisions when modelling empirical data, which may in turn shape our understanding of actions.