CdSe/CdS colloidal nanocrystals are members of a novel class of light-emitting nanoparticles with remarkable optical properties such as suppressed fluorescence blinking and enhanced emission from multiexciton states. These properties have been linked to the suppression of non-radiative Auger recombination. In this work we employ ultrafast spectroscopy techniques to identify optical signatures of neutral and charged excitonic and multiexcitonic states. We show that Auger recombination of biexcitons is not suppressed, while we observe optical gain and amplified spontaneous emission from multiexciton states and from long-lived charged-exciton states.