Over the past decade, numerous studies have identified tuberculosis patients in whom more than one distinct strain of Mycobacterium tuberculosis is present. While it has been shown that these mixed strain infections can reduce the probability of treatment success for individuals simultaneously harboring both drug-sensitive and drug-resistant strains, it is not yet known if and how this phenomenon impacts the long-term dynamics for tuberculosis within communities. Strain-specific differences in immunogenicity and associations with drug resistance suggest that a better understanding of how strains compete within hosts will be necessary to project the effects of mixed strain infections on the future burden of drug-sensitive and drug-resistant tuberculosis. In this paper, we develop a modeling framework that allows us to investigate mechanisms of strain competition within hosts and to assess the long-term effects of such competition on the ecology of strains in a population. These models permit us to systematically evaluate the importance of unknown parameters and to suggest priority areas for future experimental research. Despite the current scarcity of data to inform the values of several model parameters, we are able to draw important qualitative conclusions from this work. We find that mixed strain infections may promote the coexistence of drug-sensitive and drug-resistant strains in two ways. First, mixed strain infections allow a strain with a lower basic reproductive number to persist in a population where it would otherwise be outcompeted if has competitive advantages within a co-infected host. Second, some individuals progressing to phenotypically drug-sensitive tuberculosis from a state of mixed drug-sensitive and drug-resistant infection may retain small subpopulations of drug-resistant bacteria that can flourish once the host is treated with antibiotics. We propose that these types of mixed infections, by increasing the ability of low fitness drug-resistant strains to persist, may provide opportunities for compensatory mutations to accumulate and for relatively fit, highly drug-resistant strains of M. tuberculosis to emerge.