Cancer often arises through a sequence of genetic alterations.  Each of these alterations may confer a fitness advantage to the cell, resulting in a clonal expansion.  To model this process we consider a generalization of the biased voter process on a lattice which incorporates successive mutations modulating individual fitness.  We will study the rate of mutant spread and accumulation of oncogenic mutations in this process.  We then investigate the geometry and extent of premalignant fields surrounding primary tumors, and evaluate how the risk of secondary tumors arising from these fields may depend on the cancer progression pathway and tissue type.  (joint work w/K. Leder, R. Durrett, and M. Ryser).