Electrophoretic deposition (EPD) is a powerful technique to assemble carbon nanotube (CNT) coatings and composite films with controlled architectures. This comprehensive review of the EPD of CNTs and CNT-containing composites focuses on achievements within the last 15 years and ongoing challenges. Stable CNT suspensions are a pre-requisite for successful EPD and have been prepared by a variety of strategies, discussed here. The resulting film microstructure is determined by the initial feedstock, the suspension, and the EPD approach applied, as well as a variety of EPD processing parameters. Nanocomposites can be prepared via co-deposition, sequential deposition, or post-deposition treatments, to introduce metallic, ceramic or polymeric phases. There are numerous potential applications for both homogeneous and patterned CNT films, including as structural reinforcements for composites, as field emission, energy storage and conversion devices, as well as in biomedical applications. The advantages and disadvantages of EPD processing in these contexts are discussed.