Vif_IIIB, which has been a standard model for the viral infectivity factor of human immunodeficiency virus type 1 (HIV-1), binds the cytidine deaminase APOBEC3G (A3G) and induces its degradation, thereby precluding its lethal incorporation into assembling virions. Additionally, Vif_IIIB less efficiently degrades A3F, another potent anti-HIV-1 cytidine deaminase. Although the APOBEC3 paralogs A3A, A3B, and A3C have weaker anti-HIV-1 activities and are only partially degraded by Vif_IIIB, we found that Vif_IIIB induces their emigration from the nucleus to the cytosol and thereby causes net increases in the cytosolic concentrations and anti-HIV-1 activities of A3A and A3B. In contrast, some other Vifs, exemplified by Vif_HXB2 and Vif_ELI-1, much more efficiently degrade and thereby neutralize all APOBEC3s. Studies focused mainly on A3F imply that it occurs associated with mRNA-PABP1 in translationally active polysomes and to a lesser extent in mRNA processing bodies (P-bodies). A3F appears to stabilize the P-bodies with which it is associated. A correspondingly small proportion of Vif_IIIB also localizes in P-bodies in an A3F-dependent manner. Stress causes A3A, A3B, A3C, and A3F to colocalize efficiently with Vif_IIIB and mRNA-PABP1 complexes in stress granules in a manner that is prevented by cycloheximide, an inhibitor of translational elongation. Coimmunoprecipitation studies suggest that Vifs from different HIV-1 isolates associate with all tested APOBEC3s. Thus, Vifs interact closely with structurally diverse APOBEC3s, with effects on their subcellular localization, degradation rates, and antiviral activities. Cytosolic APOBEC3-Vif complexes are predominantly bound to mRNAs that dynamically move between translationally active and storage or processing pools.