This talk summarizes the explorations of theories beyond the Standard Model with lattice simulations. After a brief comment on the current status of the Standard Model extensions, the essential contribution made by numerical simulations in various approaches is discussed. This poses new challenges for simulation methods. The interplay with new theories gives rise to more general theoretical considerations that establish a close relationship with investigations of fundamental concepts such as gauge/gravity duality, confinement, or renormalization group flow.
Recent results presented at this conference are discussed, which include in particular composite Dark Matter models, Sp(4) gauge theory, gauge theories at the lower end of the conformal window, and supersymmetric gauge theories.