Please note different day.   A sheaf F on a polarized variety (X,O_X(1)) is ACM if F(k) has no intermediate cohomology for any integer k. The variety X is ACM if O_X is ACM. One important class of ACM bundles is the class of Ulrich bundles. An Ulrich bundle is a globally generated ACM bundle which has the largest possible space of global sections in a certain sense. Spinor bundles on quadrics are a familiar example of Ulrich bundles. It is an important problem to understand whether or not a smooth projective variety admits an Ulrich bundle, even in dimension two. In this talk, I will describe striking links between Ulrich bundles and problems in commutative algebra and representation theory. I will also discuss some partial progress on the existence problem with R. Kulkarni and Y. Mustopa where we construct vector bundles on every ACM surface that are Ulrich along a general hyperplane section.