A hyperoperation is a mapping from a domain to the powerset of the domain. Hyperoperations can be composed together to form new hyperoperations, and the resulting sets are called hyperclones. In this paper we study the lattice of restriction-closed hyperclones over finite domains. Such hyperclones form a natural subclass of hyperclones but have received comparably little attention. We give a complete description of restriction-closed hyperclones, relative to the clone lattice, and also outline some important open questions to resolve when studying hyperclones over partially defined operations.