Colloids are abundant in nature, science, and technology, with examples ranging from milk to quantum dots and the colloidal atom paradigm. Similarly, liquid crystal ordering is important in contexts ranging from biological membranes to laboratory models of cosmic strings and liquid crystal displays in consumer devices. Some of the most exciting recent developments in both of these soft matter fields emerge at their interface, in the fast-growing research arena of liquid crystal colloids. Mesoscale self-assembly in such systems may lead to artificial materials and to structures with emergent physical behavior arising from patterning of molecular order and nano- or microparticles into precisely controlled configurations. Liquid crystal colloids show exceptional promise for new discovery that may impinge on composite material fabrication, low-dimensional topology, photonics, and so on. Starting from physical underpinnings, I review the state of the art in this fast-growing field, with a focus on its scientific and technological potential.