Severe plastic deformation of solids is relevant to many materials processing techniques as well as tribological events such as wear. It results in microstructural refinement, redistribution of phases, and ultimately even mixing. However, mostly due to inability to experimentally capture the dynamics of deformation, the underlying physical mechanisms remain elusive. Here, we introduce a strategy that reveals details of morphological evolution upon shearing up to ultrahigh strains. Our experiments on metallic multilayers find that mechanically stronger layers either fold in a quasi-regular manner and subsequently evolve into periodic vortices, or delaminate into finer layers before mixing takes place. Numerical simulations performed by treating the phases as nonlinear viscous fluids reproduce the experimental findings and reveal the origin for emergence of a wealth of morphologies in deforming solids. They show that the same instability that causes kilometer-thick rock layers to fold on geological timescales is acting here at micrometer level.