Minimal surfaces are solutions of the most basic variational problem in submanifold theory, that of extremizing the area. These surfaces have been intensely studied for the past 250 years and have found striking applications in other fields of mathematics. We plan to discuss the basic variational theory of these objects, including the questions of existence and regularity. We will talk about unstable minimal surfaces obtained by min-max methods and their recent impact on the field. This includes in particular the solution to the Willmore Conjecture (1965).