Survival analysis is a major tool in cancer research, with a wide application in modeling a variety of cancer survival time data. The family of hypertabastic models includes the hypertabastic proportional hazards model and the hypertabastic accelerated failure model. The hypertabastic survival model has been applied to analysis of various types of cancer data including breast cancer, multiple myeloma, and glioma and to the analysis of non-cancer data. In the area of medical genomics, Tabatabai et al analyzed breast cancer data using clinical and multiple gene expression variables using the hypertabastic proportional hazards model and compared the results with Cox regression. Compared with Cox regression, the increase in accuracy was complemented by the capacity to analyze the time course of disease progression using the explicitly described hazard and survival functions. Recently the hypertabastic accelerated failure models have also been used to analyze mylar-polyurethane insulation data. This gives a new dimension in the application of hypertabastic survival models in biomedical settings. In his paper, we discuss the family of flexible hypertabastic models with applications in cancer.