Active site mutations that disrupt drug binding are an important mechanism of drug resistance. Such resistance causing mutations impair drug binding, thus reducing drug efficacy. Knowledge of potential resistance mutations, before they are clinically observed, would be useful in a number of ways. During the lead prioritization phase of drug development, this knowledge may direct the research team away from candidate drugs that are most likely to experience resistance. In the clinical setting, knowledge of potential resistance mutations could allow the development of treatment regimens, with drug cocktails likely to maximize efficacy. In this thesis I present a structure-based approach to predict resistance and its evolution. This method utilizes a two-pass search, which is based on a novel protein design algorithm, to identify mutations that impair drug binding while maintaining affinity for the native substrate. The approach is general and can be applied to any drug-target system where a structure of the target protein, its native substrate and the drug is available. Furthermore, it requires no training data for predictions and instead predicts resistance using structural principles. Finally, I use approximate force-field calculations from MMPBSA and simple assumptions about the relationship between binding energy and fitness to build fitness landscapes for a target protein under selective pressure from either a single drug or a drug cocktail. I use a Markov-chain based model to simulate evolution on this fitness landscape and to predict the likely evolutionary trajectories for resistance starting from a wild-type. The structure-based method was used to probe resistance in four drug-target systems: isoniazid-enoyl-ACP reductase (tuberculosis), ritonavir-HIV protease (HIV), methotrexate-dihydrofolate reductase (breast cancer and leukemia), and gleevec-ABL kinase (leukemia). This method was validated using clinically known resistance mutations for all four test systems. In all cases, it correctly predicts the majority of known resistance mutations. Furthermore, exploiting the relationship between binding energy, drug resistance and fitness of a mutant, evolution was simulated on the HIV-protease fitness landscape. This hybrid evolutionary model further improves the resistance prediction. Finally, good agreement between these evolutionary simulations and observed evolution of drug resistance in patients was found.