Embodiments relate to polycrystalline diamond (“PCD”), polycrystalline diamond compacts (“PDCs”) having a PCD table comprising such PCD, methods of fabricating such PCD and PDCs, and applications. In an embodiment, a method includes sintering diamond particles in the presence of a carbonate material to form PCD. The carbonate material includes at least one alkali metal carbonate. In an embodiment, PCD includes a plurality of bonded diamond grains defining a matrix. An interstitial constituent may be dispersed through the matrix. The interstitial constituent includes at least one alkali metal carbonate, at least one alkali metal oxide, or both. In an embodiment, a PDC includes a substrate bonded to a PCD table. The PCD table may be formed from any of the disclosed embodiments of PCD.