Abstract: A set in Euclidean space is said to be self-affine if it is the attractor of an iterated function system consisting of affine transformations. The dimension theory of general self-affine sets is not well understood. We will discuss results of the generic case and then restrict our attention to specific classes of self-affine sets where dimensions can be computed exactly. In particular, we will focus on the Hausdorff dimension of Bedford-McMullen carpets and variations thereof.