We discuss current- and noise-spectroscopy of small molecules weakly coupled to electrodes using master equations. The Coulomb interaction and size quantization effect on the molecule restrict the transport to the tunneling of single electrons. We consider situations where orbital-, spin- or vibrational excitations localized on the molecule play a role or even dominate the transport. For each case, we analyze mechanisms which lead to negative differential conductance (NDC) and even total suppression of the current. The shot noise is shown to provide additional information due to its sensitivity to asymmetries in state- and electrode- specific tunnel couplings. Combined current-noise spectroscopy could be very useful for characterization of experiments. © Springer 2006.