A brief overview of the galvanomagnetic properties of highly anisotropic cuprate superconductors is presented, with an emphasis on the internal Josephson effect, which naturally exists in multilayer HTSC crystals. The transfer of charge carriers perpendicular to the layers in such materials occurs through sequential tunneling of quasiparticles (or Cooper pairs) between well-conducting (or superconducting) CuO₂ layers through intermediate buffer layers. An analysis is made of the currently available results on nonmetallic conductivity along the c axis in the normal state, as well as data for the characteristic branched current-voltage characteristics in the superconducting state as clear experimental manifestations of tunneling effects in layered cuprate superconductors.