This chapter is dedicated to the well-know “Simulated Annealing” method, which is motivated by a physical process in metallurgy, and the fact that Nature tends to minimize the energy. The principle of the approach in the context of optimization is discussed, together with pseudocodes, and explanations of the whys. Simple and elaborated examples are presented to show the potential and efficiency of the method. A good part of the chapter is devoted to a discussion about the condition that makes Simulated Annealing find exactly the global optimal solution. However, this discussion avoids difficult mathematical developments and focuses step by step on the conditions that leads of not to convergence. Finally, this chapter introduces “Parallel Tempering”, a parallel version of Simulated Annealing which is rarely discussed and illustrated at a didactic level.