Understanding the laws governing the dark matter dynamics in the Universe is undoubtedly one of the pressing questions in astro-particle physics. While investigations of elementary particles as potential dark matter candidates have been at the heart of investigations, an equally interesting possibility arises if dark matter is instead a composite particle. I will take an overview of dark matter theories arising from extensions of Standard Model with new non-Abelian sector. Investigations of dynamics of such dark sectors benefits from connections to lattice calculations. I will sketch the avenues of progress and highlight some of the open questions in this direction. I will also take two example realisations of such strongly interacting dark matter theories and exemplify associated phenomenology.