The advent of CRISPR/Cas9-based gene editing and its demonstrated ability to streamline the development of gene drive systems has reignited interest in its application to the control of mosquitoes and the diseases they transmit. The versatility of this technology has also enabled a wide range of gene drive architectures to be realized, creating a need for their population-level and spatial dynamics to be explored. To this end, we present MGDrivE (Mosquito Gene Drive Explorer): a simulation framework designed to investigate the population dynamics of a variety of gene drive architectures and their spread through spatially-explicit mosquito populations. MGDrivE is based on a tensor algebraic generalization of the lumped age-class model of mosquito ecology. Treating these population dynamic equations in a variable-dimension tensor form allows them to be left unchanged while modifying the dimensionality of the tensor describing inheritance patterns, as required by the drive system. Spatial dynamics are accommodated through a metapopulation structure in which lumped age-class models run in parallel and migrants are exchanged between metapopulations at defined rates. Example MGDrivE simulations are presented for threshold-dependent drive systems: a) reciprocal chromosomal translocations, and b) toxin-antidote-based underdominant systems. Criteria are described for which these systems may be confined to their release community without spreading to neighboring communities.