The typical response of cancer patients to treatment is only temporary, and is often followed by relapse. The failure of various therapeutic strategies is commonly attributed to the emergence of drug resistance. The response patterns for patients under such treatments indicate that complex dynamics regulate the response of the tumour to the therapy. The environment in which the tumour lives (the stroma) is known to be a modulator of multiple mechanisms that lead to drug resistance and seems to be a likely candidate for explaining some of this complexity. Understanding the role of stromal cells in the promotion of drug resistance is critical for the design of optimal treatment strategies, and for the development of novel therapies that selectively target both the tumour and the stroma. In this thesis we design two novel mathematical models that describe cancer growth within its environment and the evolution of drug resistance within spatially complex and temporally dynamic tumours. A compartment model captures clinically observed dynamics and allows direct comparison with experimental data, facilitating model parametrisation and the understanding of inter-tumour heterogeneity. An individual cell-based model highlights the key role of local interactions, determining heterogeneity at the tissue scale, that will eventually determine treatment outcome. A non-spatial approximation of this second model allows us to find analytic guidelines for the design of effective therapy. These tools allow the simulation of a range of treatment strategies (including combination of different drugs and variation of schedule) as well as the investigation of therapy response based on patient- or organ-specic parameters. The work developed in this dissertation is based on the paradigmatic biology of melanoma and non-small cell lung cancer. Its results are therefore applicable to a variety of cancer treatments that target similar processes, and whose therapeutic failure can be attributed to environment-mediated drug resistance.