Sensorimotor learning represents a challenging problem for natural and artificial systems. Several computational models have been proposed to explain the neural and cognitive mechanisms at play in the brain. In general, these models can be decomposed in three common components: a sensory system, a motor control device and a learning framework. The latter includes the architecture, the learning rule or optimisation method, and the exploration strategy used to guide learning. In this review, we focus on imitative vocal learning, that is exemplified in song learning in birds and speech acquisition in humans. We aim to synthesise, analyse and compare the various models of vocal learning that have been proposed, highlighting their common points and differences. We first introduce the biological context, including the behavioural and physiological hallmarks of vocal learning and sketch the neural circuits involved. Then, we detail the different components of a vocal learning model and how they are implemented in the reviewed models.