Colloidal quantum dots (CQDs) are attractive materials for solar cells due to their low cost, ease of fabrication and spectral tunability. Progress in CQD photovoltaic technology over the past decade has resulted in power conversion efficiencies approaching 10%. In this review, we give an overview of this progress, and discuss limiting mechanisms and paths for future improvement in CQD solar cell technology.We briefly summarize nanoparticle synthesis and film processing methods and evaluate the optoelectronic properties of CQD films, including the crucial role that surface ligands play in materials performance. We give an overview of device architecture engineering in CQD solar cells. The compromise between carrier extraction and photon absorption in CQD photovoltaics is analyzed along with different strategies for overcoming this trade-off. We then focus on recent advances in absorption enhancement through innovative device design and the use of nanophotonics. Several light-trapping schemes, which have resulted in large increases in cell photocurrent, are described in detail. In particular, integrating plasmonic elements into CQD devices has emerged as a promising approach to enhance photon absorption through both near-field coupling and far-field scattering effects. We also discuss strategies for overcoming the single junction efficiency limits in CQD solar cells, including tandem architectures, multiple exciton generation and hybrid materials schemes. Finally, we offer a perspective on future directions for the field and the most promising paths for achieving higher device efficiencies.