Oncolytic virotherapy is new strategy for cancer treatment that relies on injecting tumors with genetically-engineered viruses that selectively infect and kill tumor cells and release immunostimulatory signals that recruit a concurrent anti-tumor immune response. Recent experiments with engineered oncolytic adenovirus have caused substantial reduction in growth rates of tumors in mice; however, the tumors always eventually relapse. By fitting time series data to mathematical models, we attempt to elucidate the underlying cancer-virus and cancer-immune dynamics to clarify the strengths and limitations of oncolytic virotherapy and suggest improved methods of treatment.