A review with 348 refs. In 1985, Car and Parrinello published a seminal article on an "Unified approach for mol. dynamics and d. functional theory". This paper established a basis for parameter-free mol. dynamics simulations in which all the interactions are calcd. on the fly via a first-principles quantum mech. method. In the 15 yr of its existence, the Car-Parrinello method has found widespread applications that expanded rapidly from physics to chem. and, most recently, even into biol. In this article, the foundations of the method in its most common implementation, the one based on d. functional theory, plane wave basis sets and pseudopotentials are described and extensions to the original scheme are outlined. The current power of Car-Parrinello simulations is illustrated by presenting selected case studies and possible future directions are sketched in the final outlook. [on SciFinder (R)]