Embodiments of the invention relate to polycrystalline diamond compacts including a substrate having a convexly-curved interfacial surface bonded to a polycrystalline diamond table. In an embodiment, a polycrystalline diamond compact includes a substrate including at least one side surface and a convexly-curved interfacial surface that may, in some embodiments, extend inwardly directly from the at least one side surface to form at least one peripheral edge therebetween. The polycrystalline diamond compact further includes a polycrystalline diamond table bonded to the convexly-curved interfacial surface of the substrate.