Behaviour recognition aims to infer the particular behaviours of the inhabitant in a smart home from a series of sensor readings from around the house. There are many reasons to recognise human behaviours; one being to monitor the elderly or cognitively impaired and detect potentially dangerous behaviours. We view the behaviour recognition problem as the task of mapping the sensory outputs to a sequence of recognised activities. This research focuses on the development of machine learning methods to find an approximation to the mapping between sensor outputs and behaviours. However, learning the mapping raises an important issue, which is that the training data is not necessarily annotated with exemplar behaviours of the inhabitant. This doctoral study takes several steps towards addressing the problem of finding an approximation to this mapping, beginning with separate investigations on current methods proposed in the literature, identifying useful sensory outputs for behaviour recognition, and concluding by proposing two directions: one using supervised learning on annotated sensory stream and one using unsupervised learning on unannotated ones.