We investigate charge dynamics in solar cells constructed using solution-processed layers of CuInS₂ (CIS) nanocrystals (NCs) as the electron donor and CdS as the electron acceptor. By using time-resolved spectroscopic techniques, we are able to observe photoinduced absorptions that we attribute to the mobile hole carriers in the NC film. In combination with transient photocurrent and photovoltage measurements, we monitor charge dynamics on time scales from 300 fs to 1 ms. Carrier dynamics are investigated for devices with CIS layers composed of either colloidally synthesized 1,3-benzenedithiol-capped nanocrystals or in situ sol-gel synthesized thin films as the active layer. We find that deep trapping of holes in the colloidal NC cells is responsible for decreases in the open-circuit voltage and fill factor as compared to those of the sol-gel synthesized CIS/CdS cell.