A central theme of the computational neuroscience research in the Biocomputation Research Group is synaptic plasticity, the activity-dependent strengthening and weakening of connections between neurons in the brain. In this talk, I will describe a number of previous PhD projects in the group that have studied computational functions, and the underlying mechanisms, of synaptic plasticity. I will focus on the functional roles and mechanisms of synaptic plasticity in the cerebellum, a brain structure that is important for the control of movements, motor learning and many higher cognitive functions. Our results suggest that different forms of synaptic plasticity at different time scales can implement many diverse functions such as associative memory, noise resistance, multiplicative operations and the transformation between different types of neural code. Moreover, I will discuss the relation between cerebellar synaptic plasticity and movement disorders that are based on cerebellar dysfunction, and I will describe the application of machine learning algorithms to analyse neuronal activity during epileptic seizures.