Building mathematical models and examining the compatibility of their theoretical predictions with empirical data are important for our understanding of evolution. The rapidly increasing amounts of genomic data on polymorphisms greatly motivate evolutionary biologists to find targets of positive selection. Although intensive mathematical and statistical studies for characterizing signatures of positive selection have been conducted to identify targets of positive selection, relatively little is known about the effects of other evolutionary forces on signatures of positive selection. In this dissertation, I investigate the effects of various evolutionary factors, including purifying selection and population demography, on signatures of positive selection. Specifically, the effects on two highly used methods for detecting positive selection, one by Wright's Fst and its analogues and the other by footprints of genetic hitchhiking, are investigated. In Chapters 2 and 3, the effect of purifying selection on Fst is studied. The results show that purifying selection intensity greatly affects Fst by modulating allele frequencies across populations. The footprints of genetic hitchhiking in a geographically structured population are studied in Chapter 4. The results demonstrate that footprints of genetic hitchhiking are significantly influenced by geographic structure, which may help scientists to infer the origin and spread of the beneficial allele. In Chapter 5, the stochastic dynamics of a hitchhiking allele are studied using the diffusion process of genetic hitchhiking conditioned on the fixation of the beneficial allele. Explicit formulae for the conditioned two-locus diffusion process of genetic hitchhiking are derived and stochastic aspects of genetic hitchhiking are investigated. The results in this dissertation show that it is essential to model the interaction of neutral and selective forces for correct identification of the targets of positive selection.