The use of preformed inorganic nanoparticles as "colloidal monomers" has received recent attention for the formation of one-dimensional (1-D) mesostructures, or "colloidal polymers." These colloidal monomers form linear assemblies through attractive, directional, interparticle interactions, which are similar to covalent or supramolecular interactions in classical polymer science. However, in contrast to the high degree of structural control available in the synthesis of classical molecular polymers, methods to control fundamental structural features such as chain length (DP), composition (copolymers), and architecture (linear, branched, etc.) are still being developed for NP-based colloidal polymer systems. We therefore review the colloidal polymerization of inorganic nanoparticle monomers by applying the conceptual framework provided by polymer science to categorize these novel systems. The descriptive nomenclature used for classical polymers is applied to NP assembly to define more explicitly the types of colloidal polymers formed in terms of DP, architecture, and composition (for binary NP assemblies). This Review includes descriptions of inorganic nanoparticle types useful for the formation of colloidal polymers with examples chosen to demonstrate control over mesoscopic structure and composition. The various emergent optical, electrical and electrochemical properties from these materials are also reviewed and correlated with structural control achieved in various colloidal polymer systems.