I work on stable homotopy theory, homological algebra, and on exporting the methods of algebraic topology to other parts of mathematics.  I have written the book "Model Categories", sometimes used as an introduction to model categories but really written in order for me to understand what properties a model category should have so that its homotopy category behaves similarly to the classical stable homotopy category. I wrote a monograph with John Palmieri and Neil Strickland about axiomatic stable homotopy theory, and another with Neil about applying these methods to the K(n)-local stable homotopy category.  I have also written about 50 papers, including "Symmetric spectra" with Brooke Shipley and Jeff Smith, the first published treatment of Jeff's construction of symmetric spectra.  I have written several papers about the category of comodules over the Hopf algebroids commonly seen in algebraic topology, and I have another series of papers, with Keir Lockridge, about the ring theory of ring spectra.