The use of agricultural fungicides exerts very strong selection pressures on plant pathogens. This can lead to the spread of fungicide resistance in the pathogen population, which leads to a reduction in efficacy of disease control and loss of yield. In this thesis, we use mathematical modelling to investigate how the spread of fungicide resistant pathogen strains can be slowed, using epidemiological models to understand how application strategies can be optimised. A range of different fungicide application strategies have been proposed as anti-resistance strategies. Two of the most often considered strategies rely on combining two fungicides with different modes of action. The first involves spraying the two fungicides at the same time (mixture) and the second spraying them alternately at different times (alternation). These strategies have been compared both experimentally and by mathematical modellers for decades, but no firm conclusion as to which is better has been reached, although mixtures have in general often been favoured. We use mathematical models of septoria leaf blotch (Zymoseptoria tritici) on winter wheat and powdery mildew on grapevine (Erysiphe necator) to investigate the relative performance of these two strategies. We show that depending on the exact way in which the strategies are compared and the exact case, either strategy can be the more effective. However, when aiming to optimise yield in the long-term, we show that mixtures are very likely to be the most effective strategy in any given case. The structure of mathematical models clearly impacts on the conclusions of those models. As well as investigating the sensitivity of our conclusions to the structure of the models, we use a range of nested models to isolate mechanisms driving the differential performance of fungicide mixtures and alternation. Although the fine detail of a model’s predictions depends on its exact structure, we find a number of conserved patterns. In particular we find no case in which mixtures do not produce the overall largest yield over the time for which the fungicide remains effective. We also investigate the effects of the timing of an individual fungicide spray on its contribution toward resistance development and disease control. A set of so-called “governing principles” to understand the performance of resistance-management strategies was recently introduced by van den Bosch et al., formalising concepts from earlier literature. These quantify selection rates by examining the difference between the growth rates of fungicide-sensitive and fungicide resistant pathogen strains. Throughout the thesis, we concentrate on the extent to which these governing principles can be used to explain the relative performance of the resistance-management strategies that are considered.