With the increasingly widespread use of high-throughput genome sequencing, the amount of biological sequence data is growing at a rate much faster than the decrease in the cost of storage media. To avoid saturating available storage capacity, such data must be compressed at a high ratio. The goal of this project is to provide a principled approach to biological data compression by developing and leveraging mutation models that approximate the generation process of genomic sequences. These models are then studied from an information-theoretic point of view to determine their combinatorial and stochastic capacities, thus providing bounds on the compressibility of genomic sequences.