The interpretation of scanning tunneling microscopy (STM) images of adsorbed molecules requires a redefinition of the current, that goes beyond the limitations imposed by the Transfer Hamiltonian formalism. Here we discuss two expressions for the tunneling current we derived, both suitable for situations in which an adsorbate is placed between tip and substrate. The former is still based on a perturbative approach, but emphasizes the contributions to the STM current due to the adsorbate. The latter is an exact expression obtained by treating the STM current like an electron transport process. This allows the inclusion of both the quantum aspects of the transport and thermal effects, and it can be used in widely different situations.