The talk will overview three recent works that make use of the notion of free energy to establish mathematical properties of some complex fluid models. The first work (in collaboration with B. Jourdain, T. Lelievre and F. Otto) studies the long-time behaviour of the solution to some multiscale models. The second work (by D. Hu and T. Lelievre) introduces a notion of free energy for purely macroscopic models. The third work (by S. Boyaval, T. Lelievre and C. Mangoubi) makes uses of the free energy to derive better numerical approaches.