Lanthanide-doped upconversion nanocrystals enable anti-Stokes emission with pump intensities several orders of magnitude lower than required by conventional nonlinear optical techniques. Their exceptional properties, namely large anti-Stokes shifts, sharp emission spectra and long excited-state lifetimes, have led to a diversity of applications. Here, we review upconversion nanocrystals from the perspective of fundamental concepts and examine the technical challenges in relation to emission colour tuning and luminescence enhancement. In particular, we highlight the advances in functionalization strategies that enable the broad utility of upconversion nanocrystals for multimodal imaging, cancer therapy, volumetric displays and photonics.