Climate models are mathematical representations of the Earth that help us predict changes in the climate. They take into account conditions affecting the main processes in our climate system; these effects are based on observations and on established physical laws such as the conservation of mass, energy, and momentum. In the present chapter, we focus on how climate models work (i.e. components of climate models, numerical resolution of basic equations, input and output data, and validation of model outputs) and then we summarize the major strengths and limitations of current climate modeling.