Abstract: "Active solids consume energy to allow for actuation and shape change not possible in equilibrium. In this talk, I will focus on the elasticity of systems as wide-ranging as far-from-equilibrium hydrogels, nanoparticles, and mechanical structures composed of active robotic components. First, I will introduce our recent work on hydrogel spheres being lowered onto a hot plate [1]. As the bottom vaporises, the resulting flow couples tightly to elastic deformations within the sphere, giving either spontaneous bouncing or steady-state floating as manifestation of the so-called elastic Leidenfrost effect. I will present theory and simulations of the floating case, which demonstrate a remarkable phenomenon: the heavier the solid, the higher it floats. I will then discuss the general competition between active boundary stresses and an elastic bulk, giving rise to shape change via so-called active elastocapillarity [2]. These results provide theoretical underpinning for recent experiments and point to the design of novel soft machines.