Magnetism in graphene is an emerging field that has received much theoretical attention. In particular, there have been exciting predictions for induced magnetism through proximity to a ferromagnetic insulator as well as through localized dopants and defects. Here, the authors discuss their experimental work using molecular beam epitaxy to modify the surface of graphene and induce novel spin-dependent phenomena. First, they investigate the epitaxial growth of the ferromagnetic insulator EuO on graphene and discuss possible scenarios for realizing exchange splitting and exchange fields by ferromagnetic insulators. Second, they investigate the properties of magnetic moments in graphene originating from localized pz-orbital defects (i.e., adsorbed hydrogen atoms). The behavior of these magnetic moments is studied using nonlocal spin transport to directly probe the spin-degree of freedom of the defect-induced states. They also report the presence of enhanced electron g-factors caused by the exchange fields present in the system. Importantly, the exchange field is found to be highly gate dependent, with decreasing g-factors with increasing carrier densities.