  Active solids consume energy to allow for actuation, shape change, and wave
propagation not possible in equilibrium. Whereas active interfaces have been
realized across many experimental systems, control of three-dimensional (3D)
bulk materials remains a challenge. Here, we develop continuum theory and
microscopic simulations that describe a 3D soft solid whose boundary
experiences active surface stresses. The competition between active boundary
and elastic bulk yields a broad range of previously unexplored phenomena, which
are demonstrations of so-called active elastocapillarity. In contrast to thin
shells and vesicles, we discover that bulk 3D elasticity controls snap-through
transitions between different anisotropic shapes. These transitions meet at a
critical point, allowing a universal classification via Landau theory. The
active surface modifies elastic wave propagation to allow zero, or even
negative, group velocities. These phenomena offer robust principles for
programming shape change and functionality into active solids, from robotic
metamaterials down to shape-shifting nanoparticles.
