We build models where Dark Matter candidates arise as composite states of a new confining gauge force, stable thanks to accidental symmetries. Restricting to renormalizable theories compatible with SU(5) unification, we find 13 models based on SU( N ) gauge theories and 9 based on SO( N ). We also describe other models that require non-renormalizable interactions. The two gauge groups lead to distinctive phenomenologies: SU( N ) theories give complex DM, with potentially observable electric and magnetic dipole moments that lead to peculiar spin-independent cross sections; SO( N ) theories give real DM, with challenging spin-dependent cross sections or inelastic scatterings. Models with Yukawa couplings also give rise to spin-independent direct detection mediated by the Higgs boson and to electric dipole moments for the electron. In some models DM has higher spin. Each model predicts a specific set of lighter composite scalars, possibly observable at colliders.