Foams, dispersions of gas bubbles in a fluid, are an example of complex out-of-equilibrium systems. The structure and properties of liquid foams are controlled by capillarity, so how foams flow or how they evolve in time depends mainly on the properties of their interfaces. In recent years there has been growing interest in “elastocapillary” foams, where bubbles are embedded in a soft solid. The properties of such foams are controlled by a competition between surface effects and bulk rheology (capillarity vs. elasticity), which can lead to a novel class of structural evolution and bubble topology, as shown in the photographs of quasi-2D foams below. Our objective is to rationalize the relation between the rheological properties of the continuous phase and the dynamics of the system.