This talk concerns a theory of "multiparameter singular integrals." The Calderon-Zygmund theory of singular integrals is a well developed and general theory of singular integrals--in it, singular integrals are associated to an underlying family of "balls" B(x,r) on the ambient space. We talk about generalizations where these balls depend on more than one "radius" parameter B(x,r_1,r_2,\ldots, r_k). These generalizations contain the classical "product theory" of singular integrals as well as the well-studied "flag kernels," but also include more general examples. Depending on the assumptions one places on the balls, different aspects of the Calderon-Zygmund theory generalize.