The main goal of the ULTRA project is the study of energy conversion and dissipation, as well as plasma heating, in turbulent nearly-collisionless plasmas, such as the solar wind or the Earth’s magnetosphere. In particular, the project aims at investigating the phase-space plasma dynamics, enabled by the weak collisionality, in conditions relevant to space and astrophysical plasmas.Characterizing the plasma dynamics in the entire phase space and its connection with the processes responsible for energy conversion and dissipation could be also relevant for laboratory plasmas, often exhibiting a weakly-collisional dynamics.