Understanding the evolution of drug resistance in malaria is a central area of study at the intersection of evolution and medicine. Antimalarial drug resistance is a major threat to malaria control and directly related to trends in malaria attributable mortality. Artemisinin combination therapies (ACT) are now recommended worldwide as first line treatment for uncomplicated malaria, and losing them to resistance would be a disaster for malaria control. Understanding the emergence and spread of antimalarial drug resistance in the context of different scenarios of antimalarial drug use is essential for the development of strategies protecting ACTs. In this study, we review the basic mechanisms of resistance emergence and describe several simple equations that can be used to estimate the probabilities of de novo resistance mutations at three stages of the parasite life cycle: sporozoite, hepatic merozoite and asexual blood stages; we discuss the factors that affect parasite survival in a single host in the context of different levels of antimalarial drug use, immunity and parasitaemia. We show that in the absence of drug effects, and despite very different parasite numbers, the probability of resistance emerging at each stage is very low and similar in all stages (for example per-infection probability of 10−10–10−9 if the per-parasite chance of mutation is 10−10 per asexual division). However, under the selective pressure provided by antimalarial treatment and particularly in the presence of hyperparasitaemia, the probability of resistance emerging in the blood stage of the parasite can be approximately five orders of magnitude higher than in the absence of drugs. Detailed models built upon these basic methods should allow us to assess the relative probabilities of resistance emergence in the different phases of the parasite life cycle.