Most empirical and theoretical studies of natural selection assume the targeted variant is a single nucleotide polymorphism (SNP), which is the simplest and most abundant form of genetic variation. Yet genomes are mutationally complex. For example, microsatellites and copy number variants are characterized by mutational rates and mechanisms that are very different than the point mutation that generates SNPs. Moreover, empirical data support the hypothesis that a subset of these variants are functional and therefore potential targets of natural selection. Despite this evidence, models of selection for these mutationally complex variants are lacking. Here, we use microsatellites as a model system to investigate natural selection that targets mutationally complex variants. We develop a realistic model of microsatellite mutation that incorporates length-dependent mutation rate, contraction bias, and multi-step mutation. We then develop models of the genotypic fitness surface for a diploid organism at a mutliallelic microsatellite. A rapid algorithm for simulating non-neutral microsatellite evolution under these models is described and used to perform inference in the framework of approximate Bayesian computation (ABC). Simulation-based assessments show that this ABC-based inference provides high power to discriminate between selection and neutrality but less power to discriminate between distinct models of selection. Applying ABC-based inference to human microsatellite data at six candidate microsatellites, we obtain strong support for selection at all six loci. We also explore the effects of direct microsatellite selection on linked sequence variation and find that summaries of the site frequency spectrum provide little power to detect microsatellite selection. However, when conditioned on the number of segregating sites, the number of haplotypes provides high power to detect microsatellite selection. Interestingly, this statistic is most effective at detecting selection on highly mutable microsatellites, yet bears near-zero power to detect hard sweeps. Together, these results suggest that a scan for microsatellite selection is feasible, provided that an appropriate null model is used to simulate the empirical distribution to which observed data are compared. Finally, we suggest that future efforts to detect and characterize microsatellite selection should combine summaries of microsatellite allele frequency distributions and linked sequence data.