As evolutionary cancer therapies increasingly enter clinical trials, there is an urgent need for theoretical and experimental studies to identify the patients most likely to benefit, to inform trial design, and to aid the interpretation of outcomes. I will appraise three promising treatment strategies that manipulate different aspects of intra-tumour evolution. The first strategy aims to maximize the probability that resistant cells succumb to stochastic extinction during multi-strike therapy. Whereas standard clinical practice is to wait for evidence of relapse, mathematical analysis within the framework of evolutionary rescue theory reveals that the optimal time to switch to a second treatment is when the tumour is close to its minimum size, when it is likely undetectable. Strategy two is bipolar androgen therapy, which involves cycling between extremely low and supraphysiologic levels of testosterone to steer evolutionary dynamics in castrate-resistant prostate cancer. A first mathematical model of this system suggests that the treatment schedule used in previous clinical trials can be substantially improved. For the third strategy, adaptive therapy, I will present results of a spatial stochastic model that bridges the gap between deterministic ODE systems and typically intractable agent-based simulations. This novel approach shows that the predicted benefit of adaptive therapy importantly differs between two- and three-dimensional tumours. Finally, I will share unpublished experimental data revealing how treatment-sensitive and resistant cells grow and interact during adaptive therapy using EGFR inhibitors, including precise tracking of the spatial configuration of resistant subclones within tumour spheroids using confocal microscopy.