With Bose-Einstein condensation, fermionic superfludity is one of the main paradigms in quantum many-body physics. In the early 80's, Leggett, Nozières and Schmitt-Rink suggested that they could be unified within a single model, the so-called BEC-BCS crossover describing the ground state of an ensemble of attractive fermions. In this scenario, weakly attractive fermions are described by Bardeen-Cooper and Schrieffer's (BCS) theory while in the strongly attractive regime they form a Bose-Einstein condensate of deeply bound bosonic dimers. The BEC-BCS crossover hypothesis was confirmed experimentally in 2003 using ultracold vapours. However, an accurate and comprehensive theoretical description of the properties is still missing. In my talk, I will present an overview of recent advances in the experimental and theoretical study of strongly correlated fermions. I will show how Gross-Pitaevskii equation can be extended to address the dynamics of these systems within the hydrodynamic approximation and I will discuss numerical strategies pursued to capture the dynamics of solitons or vortices in these systems.