The rapid evaporation of a superheated liquid (vapor explosion) under microgravity conditions is studied by direct numerical simulation. The time-dependent Navier-Stokes and energy equations coupled to the interface dynamics are solved using a two-dimensional finite-difference/front-tracking method. Large interface deformations, topology change, latent heat, surface tension and unequal material properties between the liquid and vapor phases are included in the simulations. A comparison of numerical results to the exact solution of a one-dimensional test problem shows excellent agreement. For the two-dimensional rapid evaporation problem, the vapor volume growth rate and unstable interface dynamics are studied for increasing levels of initial liquid superheat. As the superheat is increased the liquid-vapor interface experiences increasingly unstable energetic growth. These results indicate that heat transfer plays a very important role in the instability mechanism leading to vapor explosions. It is suggested that the Mullins-Sekerka instability could play a role in the instability initiation mechanism.