Recent research has indicated that viruses specifically infecting tumor cells could be used as an alternative therapeutic approach in cancer patients. A particular example is the adenovirus ONYX-015, which has entered clinical trials in the context of head and neck cancer. Successful therapy crucially requires an understanding about how viral and host parameters influence tumor load. The interactions between the growing tumor, the replicating virus, and possible immune responses are multifactorial and nonlinear. Hence, a complete understanding of how virus and host characteristics influence the outcome of therapy requires mathematical models. In this study, such mathematical models are presented and analyzed. The study investigates three possible scenarios that could be relevant for therapy: (a) viral cytotoxicity alone kills tumor cells; (b) a virus-specific lytic CTL response contributes to killing of infected tumor cells; (c) the virus elicits immunostimulatory signals within the tumor that promote the development of tumor-specific CTL. The models precisely define conditions required for successful therapy. They identify the parameters that need to be measured and modulated to evaluate and refine the existing therapy regimes.