We use photoinduced absorption (PIA) spectroscopy to study charge generation and recombination in a series of bulk heterojunction blends relevant to organic and hybrid solar cells. We compare both organic and inorganic electron acceptors, including the fullerene, phenyl-C-61-butyric acid methyl ester (PCBM), oxides such as ZnO and TiO2, and colloidal quantum dots, including CdSe and PbS nanocrystals. We use a variety of donor host polymers, including poly(3-hexylthiophene) (P3HT), poly[2-methoxy-5-(3’,7’-dimethyloctyloxy)-p-phenylenevinylene] (MDMO-PPV), and poly(2,3-bis(2-hexyldecyl)quinoxaline-5,8-diyl-alt-N-(2-hexyldecyl)-dith ieno-[3,2-b:2’,3’-d]pyrrole) (PDTPQx-HD). In every case, we measure longer average carrier lifetimes in blends with the inorganic acceptors as compared to blends with PCBM. The PIA data also suggest that the internal electric fields are attenuated in the inorganic blends, consistent with increased screening between the photogenerated carriers due to the higher dielectric constants of the inorganic nanopartides. Using ligand exchange experiments, we further demonstrate that surface electron trapping on the inorganic colloids contributes to at least part of the increased lifetime in the PDTPQx-HD/PbS blends and that ligand exchange to remove traps can be used to improve the performance of these polymer/low-band-gap quantum dot hybrid photovoltaics.