Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science Alessandro Laio SISSA/ISAS, Statistical and biological physics, Via Beirut 2-4 Trieste, Italy Francesco L. Gervasio Computational Science, Department of Chemistry and Applied Biosciences, ETH Z¨ urich, USI Campus, Via Giuseppe Buffi 13, CH-6900 Lugano, Switzerland. Abstract. Metadynamics is a powerful algorithm that can be used both for reconstructing the free energy and for accelerating rare events in systems described by complex Hamiltonians, at the classical or at the quantum level. In the algorithm the normal evolution of the system is biased by a history-dependent potential constructed as a sum of Gaussians centered along the trajectory followed by a suitably chosen set of collective variables. The sum of Gaussians is exploited for reconstructing iteratively an estimator of the free energy and forcing the system to escape from local minima. This review is intended to provide a comprehensive description of the algorithm, with a focus on the practical aspects that need to be addressed when one attempts to apply metadynamics to a new system: (i): the choice of the appropriate set of collective variables; (ii): the optimal choice of the metadynamics parameters; (iii): how to control the error and ensure convergence of the algorithm.