We use molecular dynamics simulations to study the role played by solvent in promoting one-dimensional (1D) growth of colloidal nanostructures. Considering the growth of Ag nanowires and nanoplates in organic solvent, we study how solvent influences the aggregation of a small and relatively isotropic nanocrystal with a larger rectangular cuboid or a square plate. We observe that when the two nanocrystals approach one another, they almost always adopt a mesocrystal configuration, in which the two particles hover next to each other with their facets parallel and one or two layers of solvent between them – analogous to experimentally observed mesocrystal structures. Nanocrystal aggregation occurs from the mesocrystal state and it is most likely to occur on the smallest facets, which perpetuates 1D growth. We observe instances of oriented attachment preferentially at the smallest facet. These studies indicate that solvent can play a key role in promoting the 1D growth of colloidal nanostructures.