The molecular evolutionary mechanisms underpinning virus-host interactions are increasingly recognized as key drivers of virus emergence, host specificity, and the likelihood that viruses can undergo a host shift that alters epidemiology and transmission biology. Zika virus (ZIKV) is mainly transmitted between humans by Aedes aegypti mosquitoes. However, the 2015 to 2017 outbreak stimulated discussion regarding the role of Culex spp. mosquitoes in transmission. Reports of ZIKV-infected Culex mosquitoes, in nature and under laboratory conditions, resulted in public and scientific confusion. We previously found that Puerto Rican ZIKV does not infect colonized Culex quinquefasciatus, Culex pipiens, or Culex tarsalis, but some studies suggest they may be competent ZIKV vectors. Therefore, we attempted to adapt ZIKV to Cx. tarsalis by serially passaging virus on cocultured Ae. aegypti (Aag2) and Cx. tarsalis (CT) cells to identify viral determinants of species specificity. Increasing fractions of CT cells resulted in decreased overall virus titer and no enhancement of Culex cell or mosquito infection. Next-generation sequencing of cocultured virus passages revealed synonymous and nonsynonymous variants throughout the genome that arose as CT cell fractions increased. We generated nine recombinant ZIKVs containing combinations of the variants of interest. None of these viruses showed increased infection of Culex cells or mosquitoes, demonstrating that variants associated with passaging were not specific to increased Culex infection. These results reveal the challenge of a virus adapting to a new host, even when pushed to adapt artificially. Importantly, they also demonstrate that while ZIKV may occasionally infect Culex mosquitoes, Aedes mosquitoes likely drive transmission and human risk. IMPORTANCE ZIKV is mainly transmitted between humans by Aedes mosquitoes. In nature, ZIKV-infected Culex mosquitoes have been found, and ZIKV infrequently infects Culex mosquitoes under laboratory conditions. Yet, most studies show that Culex mosquitoes are not competent vectors for ZIKV. We attempted to adapt ZIKV to Culex cells to identify viral determinants of species specificity. We sequenced ZIKV after it was passaged on a mixture of Aedes and Culex cells and found that it acquired many variants. We generated recombinant viruses containing combinations of the variants of interest to determine if any of these changes enhance infection in Culex cells or mosquitoes. Recombinant viruses did not show increased infection in Culex cells or mosquitoes, but some variants increased infection in Aedes cells, suggesting adaptation to those cells instead. These results reveal that arbovirus species specificity is complex, and that virus adaptation to a new genus of mosquito vectors likely requires multiple genetic changes.