Synaptic plasticity is a central theme in neuroscience. A framework of three-factor learning rules provides a powerful abstraction, helping to navigate through the abundance of models of synaptic plasticity. It is well-known that the dopamine modulation of learning is related to reward, but theoretical models predict other functional roles of the modulatory third factor; it may encode errors for supervised learning, summary statistics of the population activity for unsupervised learning or attentional feedback. Specialized structures may be needed in order to generate and propagate third factors in the neural network.