In this note we will present some existence and uniqueness issues for three coupled PDE-ODE systems. The common frame is that they arise as the asymptotical dynamics of a regular, incompressible two-dimensional flow interacting with: • points at which the vorticity is highly concentrated (point vortices); • an obstacle shrinking to a steady point; • rigid bodies contracting to moving massive particles. We will mainly focus on the last situation, corresponding to the article [11], which is a joint work with Christophe Lacave.