Climate models are used to understand the complex interactions that result in climate change as well as provide projections of future climate change and its impacts on society. I will give a broad overview of current climate and Earth system models, including the diversity of algorithms represented, the complexity of the models and their application to both science and policy problems. Future demands on climate model applications as well as a changing computing landscape will require rethinking the design and implementation of our models. I will describe some of the bigger challenges and potential paths forward.