CRISPR gene drives---genetic constructs that bias their own inheritance---offer a means to rapidly spread genetic alterations through pest populations. These alterations can confer a desirable trait, such as the inability to transmit disease in malaria-vector mosquitoes (modification drives), or cause lethality or sterility, leading to the reduction or extinction of the pest population (suppression drives). Both modification and suppression drives have been successfully demonstrated in controlled laboratory settings, but it remains unclear how they will behave if released into the wild. In this dissertation, I employ a variety of modeling approaches to systematically investigate how gene drives spread in more realistic populations shaped by ecological, spatial, and genetic factors. First, I examine how a key life history trait in plants affects gene drive dynamics. Using an individual-based model that incorporates the full life cycle of annual weeds, I show that persistent seedbanks can reduce the necessary efficiency of suppression drives by limiting population growth at low densities. Seedbanks can also increase the containment potential of threshold-dependent drives---gene drives that require a higher introduction frequency to spread than conventional drives---because they dilute the drive frequency in adult plants, effectively raising the invasion threshold. Next, I use diffusion theory and individual-based models to assess how spatial structure influences the ability of threshold-dependent drives to invade new populations. I show that invasiveness is not well-described by a binary threshold separating spread from loss but is better characterized by a range of release sizes and spatial configurations at which invasion is possible. This range varies based on drive and population parameters but is typically widest for low-threshold modification drives with small fitness costs. Lastly, I investigate how the genetic architecture of suppression drives affects the selective advantage of resistance alleles that prevent drive conversion while preserving target gene function. I propose a new multilocus design in which the drive allele is decoupled from the genes it disrupts, lowering the selective advantage for resistance alleles at the drive site. Disrupted target sites impose minor recessive deleterious fitness costs individually but generate a substantial genetic load as they accumulate. Using individual-based models, I show that this multilocus drive can maintain strong population suppression even after resistance establishes, unlike standard single-locus suppression drives, which are quickly overtaken.