Bottlebrush polymers are a type of branched or graft polymer with polymeric side-chains attached to a linear backbone, and the unusual architectures of bottlebrushes provide a number of unique and potentially useful properties. These include a high entanglement molecular weight, enabling rapid self-assembly of bottlebrush block copolymers into large domain structures, the self-assembly of bottlebrush block copolymer micelles in a selective solvent even at very low dilutions, and the functionalization of bottlebrush side-chains for recognition, imaging, or drug delivery in aqueous environments. This review article focuses on recent developments in the field of bottlebrush polymers with an emphasis on applications of bottlebrush copolymers. Bottlebrush copolymers contain two (or more) different types of polymeric side-chains. Recent work has explored the diverse properties and functions of bottlebrush polymers and copolymers in solutions, films, and melts, and applications explored include photonic materials, bottlebrush films for lithographic patterning, drug delivery, and tumor detection and imaging. We provide a brief introduction to bottlebrush synthesis and physical properties and then discuss work related to: (i) bottlebrush self-assembly in melts and bulk thin films, (ii) bottlebrushes for photonics and lithography, (iii) bottlebrushes for small molecule encapsulation and delivery in solution, and (iv) bottlebrush micelles and assemblies in solution. We briefly discuss three potential areas for future research, including developing a more quantitative model of bottlebrush self-assembly in the bulk, studying the properties of bottlebrushes at interfaces, and investigating the solution assembly of bottlebrush copolymers.