The study of collective dynamics is attracting the interest of different research fields, both due to their wide range of applications and to their ability to model self-organization. The emergence of global patterns from local interactions can be easily observed in flock of birds, schools of fish, human crowds, but also cells exhibit collective behaviors in different biological processes characterizing the human body (e.g. in embryogenesis, wound healing, immune response, tumor growth). The main feature of collective cells migration is that the emergent behavior is also driven by chemical stimuli, and not only by mechanical interactions. This course aims to give participants a brief but complete introduction to the research field of modelling and simulation of collective dynamics. Starting with a survey of influential works of the literature, recent mathematical developments and new directions and applications will be presented. A specific focus will be on different numerical techniques proposed to simulate the different kind of equations involved in the presented models.