We study viscous fluids surrounded by vacuum in the plane. For the incompressible Navier–Stokes equations, we discuss uniqueness, interface regularity and long-time behaviour for critical and finite-energy initial velocities. We then examine how removing viscosity in the vacuum changes the dynamics, allowing splash singularities, and formulate a small-data regularity question. Finally, we present numerical observations suggesting a completely different behaviour in the compressible case.