Critical homoclinic orbits lead to snap-back repellers

► We consider critical homoclinic orbits in continuous and discontinuous maps. ► Unbounded homoclinic orbits in maps on unbounded domains are considered as well. ► We show that a snapback-repeller (SBR) with a non-critical homoclinic orbit implies chaos. ► We show also that a SBR with a critical homoclinic orbit may or may not imply chaos.