A polycrystalline compact comprises a plurality of grains of hard material and a plurality of nanoparticles disposed in interstitial spaces between the plurality of grains of hard material. The nanoparticles have cores of a first material and at least one oxide material on the cores. An earth-boring tool comprises such a polycrystalline compact. A method of forming a polycrystalline compact comprises combining a plurality of hard particles with a plurality of nanoparticles to form a mixture and sintering the mixture to form a polycrystalline hard material comprising a plurality of interbonded grains of hard material. A method of forming a cutting element comprises infiltrating interstitial spaces between interbonded grains of hard material in a polycrystalline material with a plurality of nanoparticles.