Finding the global minimum of a nonconvex optimization problem is a notoriously hard task appearing in numerous applications, from signal processing to machine learning. Simulated annealing (SA) is a family of stochastic optimization methods where an artificial temperature controls the exploration of the search space while preserving convergence to the global minima. SA is efficient, easy to implement, and theoretically sound, but suffers from a slow convergence rate. The purpose of this work is twofold. First, we provide a comprehensive overview on SA and its accelerated variants. Second, we propose a novel SA scheme called curious simulated annealing, combining the assets of two recent acceleration strategies. Theoretical guarantees of this algorithm are provided. Its performance with respect to existing methods is illustrated on practical examples.