Crowds of people are gathering at multiple venues, such as concerts, political rallies, as well as in commercial malls, or just simply walking on the streets. More and more people are flocking to live in urban areas, thus generating a lot of scenarios of crowds. As a consequence, there is an increasing demand for automatic tools that can analyze and predict the behavior of crowds to ensure safety. Crowd motion analysis is a key feature in surveillance and monitoring applications, providing useful hints about potential threats to safety and security in urban and public spaces. It is well known that people gatherings are generally difficult to model, due to the diversity of the agents composing the crowd. Each individual is unique, being driven not only by the destination but also by personality traits and attitude. The domain of crowd analysis has been widely investigated in the literature. However, crowd gatherings have sometimes resulted in dangerous scenarios in recent years, such as stampedes or during dangerous situations. To take a step toward ensuring the safety of crowds, in this work we investigate two main research problems: we try to predict each person future position and we try to understand which are the key factors for simulating crowds. Predicting in advance how a mass of people will fare in a given space would help in ensuring the safety of public gatherings.