Abundant evidence indicates that dark matter accounts for most of the matter in the universe, but its fundamental nature remains unknown. I will discuss the intriguing possibility that dark matter may consist of composite particles arising from a new strongly interacting sector. After reviewing the motivations for and main features of composite dark matter, I will explain the role of lattice field theory as a means to obtain non-perturbative predictions of its properties. Such lattice calculations are needed to translate experimental results (from particle colliders, large underground detectors, and future gravitational-wave observatories) into constraints on composite dark matter.