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Ab initio or first-principles methods have emerged in the last two decades as a powerful tool to probe the properties of matter at the microscopic scale. These approaches are used to derive macroscopic observables under the controlled condition of a "computational experiment," and with a predictive power rooted in the quantum-mechanical description of interacting atoms and electrons. Density-functional theory (DFT) has become de facto the method of choice for most applications, due to its combination of reasonable scaling with system size and good accuracy in reproducing most ground state properties. Such an electronic-structure approach can then be combined with classical molecular dynamics to provide an accurate description of thermodynamic properties and phase stability, atomic dynamics, and chemical reactions, or as a tool to sample the features of a potential energy surface. In a molecular-dynamics (MD) simulation the microscopic trajectory of each individual atom in the system is determined by integration of Newton's equations of motion. In classical MD, the system is considered composed of massive, point-like nuclei, with forces acting between them derived from empirical effective potentials. Ab initio MD maintains the same assumption of treating atomic nuclei as classical particles; however, the forces acting on them are considered quantum mechanical in nature, and are derived from an electronic-structure calculation. The approximation of treating quantummechanically only the electronic subsystem is usually perfectly appropriate, due to the large difference in mass between electrons and nuclei. Nevertheless, nuclear quantum effects can be sometimes relevant, especially for light elements such as hydrogen; classical or ab initio path integral approaches can then be applied, albeit at a higher computational cost. The use of Newton's equations of motion for the nuclear evolution implies that vibrational degrees of freedom are not quantized, and will follow a Boltzmann statistics. This approximation becomes fully justified only for temperatures comparable with the highest vibrational level in the system considered. [ABSTRACT FROM AUTHOR]