We reconsider the old problem of the dynamics of spontaneous symmetry breaking (SSB) using 3D lattice simulations. We develop a theory of tachyonic preheating, which occurs due to the spinodal instability of the scalar field. Tachyonic preheating is so efficient that SSB typically completes within a single oscillation as the field rolls towards the minimum of its effective potential. We show that, contrary to previous expectations, preheating in hybrid inflation is typically tachyonic. Our results may also be relevant for the theory of the formation of topological defects and of disoriented chiral condensates in heavy ion collisions.