We explore the application and usefulness of the heavy quark symmetry to describe the weak decays of hadrons (mesons and baryons) containing two heavy quarks. Firstly, we address the internal dynamics of a heavy-heavy bound system with the help of estimates based on potential models, showing an approximate spin symmetry in the preasymptotic quark mass region including charmonium, bottonium and Bc meson states. However, no asymptotic spin symmetry should hold in the infinite quark mass limit in contrast to singly heavy hadrons. Predictions on semileptonic and two-body nonleptonic decays of Bc mesons are shown. Furthermore, the flavor and spin symmetries stemming from the interaction between the heavy and light components in hadrons (combining in a "superflavor" symmetry) permit a classification in meson- type supermultiplets containing singly heavy mesons together with doubly heavy baryons, and baryon-type supermultiplets containing singly heavy baryons together with some exotic doubly heavy multiquark states (diquonia). Exploiting their well-defined transformation properties under the superflavor symmetry group, we get predictions on the widths for some semileptonic and two-body nonleptonic decays of baryons containing both b- and c-quarks.