In this talk, we investigate and classify finite (simple) regular hom-(Lie) groups. By group theory, we derive a series of simplicity theorems that are used to classify finite simple regular hom-groups. By automorphism groups and conjugacy classes, we also classify finite regular hom-groups of significantly high order. Inspired by the classical methods for classifying Lie groups and establish a one-to-one correspondence between simply-connected regular hom-Lie groups and regular hom-Lie algebras. Using an approach analogous to the classification of simple regular hom-groups, we classify simple regular hom-Lie algebras, and thereby classify simply-connected simple regular hom-Lie groups.