In this talk, I will discuss some recent progress on the equilibration (i.e., convergence to equilibrium as time goes to infinity) of some first order PDE models with a gradient flow structure. Such models arise naturally from biological and social sciences, as the description of the collective dynamics of a large group of individuals. Typical examples include the aggregation-diffusion equation and the aggregation equation with attractive-repulsive pairwise interactions. I will introduce a few important concepts and methods in the proof of equilibration, including the tightness of solutions, estimates of energy dissipation rates, and convexity arguments for the uniqueness of steady state.  

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