Cancers are complex and heterogeneous pathological "organs" in a dynamic interplay with their host. Models of human cancer in vitro, used in cancer biology and drug discovery, are generally highly reductionist. These cancer models do not incorporate complexity or heterogeneity. This raises the question as to whether the cancer models' biochemical circuitry (not their genome) represents, with sufficient fidelity, a tumor in situ. Around 95% of new anticancer drugs eventually fail in clinical trial, despite robust indications of activity in existing in vitro pre-clinical models. Innovative models are required that better capture tumor biology. An important feature of all tissues, and tumors, is that cells grow in three dimensions. Advances in generating and characterizing simple and complex (with added stromal components) three-dimensional in vitro models (3D models) are reviewed in this article. The application of stirred bioreactors to permit both scale-up/scale-down of these cancer models and, importantly, methods to permit controlled changes in environment (pH, nutrients, and oxygen) are also described. The challenges of generating thin tumor slices, their utility, and potential advantages and disadvantages are discussed. These in vitro/ex vivo models represent a distinct move to capture the realities of tumor biology in situ, but significant characterization work still remains to be done in order to show that their biochemical circuitry accurately reflects that of a tumor.