Midbrain dopaminergic (DA) neurons fire bursts of activity in response to sensory stimuli, including those associated with primary reward. They are therefore conditional bursters - the bursts conveying, amongst other things, motivationally relevant information to the forebrain. In the forebrain, bursts give rise to a supra-additive release of dopamine, and possibly favour the release of co-localised neuropeptides. Evidence is presented that in rat DA neurons, bursts are engendered by the activity of cortically-regulated afferents. Certain factors are identified which, in combination, lead to burst production: (1) A burst of activity in EAAergic afferents to DA neurons arising from non-cortical sources, but controlled by the medial prefrontal cortex; (2) N-methyl-D-aspartate receptor activation, producing a slow depolarising wave in the recipient neuron; (3) activation of a high threshold, dendritically located calcium conductance which produces a 'plateau potential'; (4) activation of a calcium-activated potassium conductance, which terminates the burst. These factors are argued to operate in the context of an 'optimal' level of intracellular calcium buffering for bursting. Other factors which appear to be involved in bursting in other systems, in particular a low threshold calcium conductance, are rejected as being necessary for bursting in DA neurons. The factors which do play a crucial role in burst production in DA neurons are integrated into a theory from which arises a series of hypotheses amenable to empirical investigation. Additional factors are discussed which may modulate bursting. These may either act indirectly through changes in membrane potential (or intracellular calcium concentration), or they may act directly through an interaction with certain conductances, which appear to promote or inhibit burst firing in DA neurons.