We discuss the multi-configuration time-dependent Hartree (MCTDH) method for the approximation of the time-dependent Schrödinger equation in quantum molecular dynamics. This method approximates the high-dimensional wave function by a linear combination of products of functions depending only on a single degree of freedom. The equations of motion, obtained via the Dirac-Frenkel time-dependent variational principle, consist of a coupled system of ordinary and low-dimensional nonlinear partial differential equations. We show that the MCTDH equations are well-posed as long as a full-rank condition remains satisfied. The solution is shown to be regular enough to ensure quasi-optimality of the approximation over short time intervals and to admit an efficient numerical treatment if the potential is sufficiently smooth.