Composite Higgs models describe physics beyond the Standard Model in terms of new strongly-interacting sectors. Lattice field theory provides the tools to study the dynamics of such sectors from first principles if a UV completion of the model exists. On one hand viable UV completions must be compatible with the constraints coming from experimental data, while on the other hand having a UV completion has very stringent consequences for the dynamics. Recent lattice studies have investigated a variety of theories trying to characterise their properties, and understand the potential phenomenological implications. I will review a number of examples, and discuss potential future directions.