In this seminar, I will discuss integrable systems called affine Gaudin models and their application to the study of integrable sigma models. As an introductory example, I will first discuss a simpler class of Gaudin models, the finite ones, and their relation with integrable spin chains and mechanical systems. I will then explain how to use affine Gaudin models to construct new integrable classical sigma models, by coupling together an arbitrary number of principal chiral models with Wess-Zumino terms.