We investigate the charge-trapping dynamics in hybrid nanocrystal-polymer systems and their effect on performance in photovoltaic devices. Employing various steady-state spectroscopy techniques and ultrafast, three-pulse transient absorption methods, we identify the depth of electron trap states in the nanocrystal band gap and measure their population dynamics. Our findings show that photogenerated electrons are trapped at midgap states on the nanocrystal within hundreds of picoseconds. The trapping of the majority of charge carriers before charge extraction results in a lowering of the quasi-Fermi level of the electrons which limits the device open-circuit voltage, thereby underlining the significance of these processes in conjugated polymer/nanocrystal hybrid photovoltaics.