The establishment and refinement of neural circuits involve both the formation of new connections and the elimination of already existing connections. Elimination of connections occurs, for example, in the development of mononeural innervation of muscle fibres and in the formation of ocular dominance columns in the visual cortex. The process that leads to the elimination of connections is often referred to as axonal or synaptic competition. Although the notion of competition is commonly used, the process is not well understood-with respect to, for example, the type of competition, what axons and synapses are competing for, and the role of electrical activity. This article reviews the types of competition that have been distinguished and the models of competition that have been proposed. Models of both the neuromuscular system and the visual system are described. For each of these models, the assumptions on which it is based, its mathematical structure, and the extent to which it is supported by the experimental data are evaluated. Special attention is given to the different modelling approaches and the role of electrical activity in competition.