Aedes albopictus mosquitoes have been experimentally demonstrated to be a competent vector for Zika virus (ZIKV) in different countries, but there are still some gaps related to the importance of Ae. albopictus in ZIKV transmission. Recent studies on Spanish Ae. albopictus populations showed controversial results for ZIKV transmission and no studies have been performed yet to detect infectious ZIKV in saliva of progeny of infected female mosquitoes. Herein, the horizontal transmission (HT) and vertical transmission (VT) of ZIKV in field-collected Ae. albopictus mosquitoes from Spain were evaluated for ZIKV strains (African I and Asian lineages) to better estimate the risk of ZIKV transmission by Ae. albopictus. The two field-collected Ae. albopictus populations assayed were infected by all tested ZIKV strains, however differences in terms of vector competence were detected depending on strain-population combination. Moreover, a higher susceptibility to the African I lineage strain than to the Asian lineage strain was observed in both mosquito populations. On the other hand, VT was demonstrated for both ZIKV lineages, detecting the virus in both males and females of the progeny of infected females, although importantly ZIKV dissemination and transmission were not detected in the infected females from the offspring. The results of the present study demonstrate that Spanish Ae. albopictus populations could sustain virus transmission in case of ZIKV introduction, but VT would play a poor role in the ZIKV epidemiology. Overall, our results provide helpful information to health authorities to establish efficient surveillance and vector control programmes for ZIKV.