following colding and minicozzi, we consider the entropy of (hyper)-surfaces in euclidean space. this is a numerical measure of the geometric complexity of the surface. in addition, this quantity is intimately tied to to the singularity formation of the mean curvature flow which is a natural geometric heat flow of submanifolds. in the talk, i will discuss several results that show that closed surfaces for which the entropy is small are simple in various senses. this is all joint work with l. wang.