Nuclei containing a charm quark have been predicted theoretically since 1977, and are described as charmed hypernuclei despite the possible absence of strange quarks. In particular, the lightest charmed baryons, the Λ c and Σ c baryons, are predicted to exist in bound states in charmed hypernuclei, and could be created in processes analogous to those used to make hypernuclei. The depth of the Λ c potential in nuclear matter is predicted to be 58 MeV, but unlike Λ hypernuclei, larger hypernuclei containing the positively charged Λ c would be less stable than the corresponding Λ hypernuclei due to Coulomb repulsion. The mass difference between the Λ c and the Σ c is too large for appreciable mixing of these baryons to occur in hypernuclei. Weak decays of charmed hypernuclei have strong relativistic corrections compared to those in ordinary hypernuclei, as the energy released in the decay process is comparable to the mass of the Λ baryon.