The idea of driving an engineered gene to fixation in a population is more than 40 years old. Its potential applications are ambitious and widely varied, including the eradication of disease vectors, the control of pest species, and the preservation of endangered species from extinction. So far, all proposed drive mechanisms have fallen short of these goals. The recently developed CRISPR/Cas9-mediated gene drive (CMGD) now promises a mechanism for quickly driving genetically modified alleles to high frequency in a population regardless of their fitness cost. However, we still lack a comprehensive understanding of the population dynamics of CMGD and are therefore unable to predict its spread in natural populations in the face of potential resistance. Here we develop a comprehensive population-genetic model of CMGD to evaluate the feasibility of this process in natural populations. We specifically study the probability that resistance evolves against a gene drive from alleles that (i) are already present as standing genetic variation when the driver allele is introduced into the population, (ii) arise by de novo mutations while the driver allele is spreading through the population, or (iii) are created by the drive itself when double strand break repair results in mutated target sites that can no longer be recognized by the driver's guide RNA. We use these results to analyze how different drive strategies (breaking a gene versus editing/inserting a gene) are expected to influence the probability of resistance due to different fitness costs of resistance alleles. We finally discuss how our results can be used to identify strategies with reduced potential for resistance evolution in order to facilitate a successful drive, as well as approaches that would promote resistance as a possible mechanism for controlling the spread of a drive.