A Calabi-Yau is compact complex manifold with trivial canonical bundle and vanishing intermediate cohomologies of its structure sheaf.  For example, a Calabi-Yau 1-fold is an elliptic curve, and a Calabi-Yau 2-fold is a K3 surface.  Conventionally, "Calabi-Yau" refers to higher dimensional varieties.  In this talk, we'll discuss similarities and differences between Calabi-Yau 2-folds (K3 surfaces) and higher dimensional ones.