Studying the long term orbital evolution of a small body is a quite difficult task because of multiple planetary encounters and non-gravitational forces. However, the precise computation and propagation of an asteroid orbit is essential, not only for scientific purpose, but also for planetary protection. Here we present the Italian project MONASTER (MONitoring ASTERoids) dealing with asteroid dynamics and impacts prediction. The project, established thanks to Italian Space Agency funding, will start in late Autumn and it aims to develop innovative mathematical models and algorithms to face the new era of observations and discoveries. The talk will describe the structure of the project and some initial results; moreover some research works that fit perfectly in the spirit of the MONASTER project (dealing with Yarkovsky effect and tools for imminent impactors) will be shown and discussed.