The objective of this tutorial is to provide participants with an accessible introduction to mixture models (MMs) and hidden Markov models (HMMs) and the necessary skills to apply them in their own research. These models are particularly useful to analyse aspects of cognition which are best understood in terms of discrete types and states (e.g., when people are expected to apply distinct strategies when performing a task). MMs and HMMs allow one to extract such types/states even when they are not known exactly beforehand. We will provide an intuitive introduction to the underlying theory of MMs and HMMs and will show how to apply the models in practice using freely available software. Throughout the tutorial, the techniques are illustrated with real data relevant to a cognitive science audience. Participants are encouraged to bring their laptop to follow the examples and apply the techniques to their own data.