Dengue virus (DENV, family Flaviviridae, genus Flavivirus) exists as four distinct serotypes. Generally, immunity after infection with one serotype is protective and lifelong, though exceptions have been described. However, secondary infection with a different serotype can result in more severe disease for a minority of patients. Host responses to the first DENV infection involve the development of both cross-reactive antibody and T cell responses, which, depending upon their precise balance, may mediate protection or enhance disease upon secondary infection with a different serotype. Abundant evidence now exists that responses elicited by DENV infection can cross-react with other members of the genus Flavivirus, particularly Zika virus (ZIKV). Cohort studies have shown that prior DENV immunity is associated with protection against Zika. Cross-reactive antibody responses may enhance infection with flaviviruses, which likely accounts for the cases of severe disease seen during secondary DENV infections. Data for T cell responses are contradictory, and even though cross-reactive T cell responses exist, their clinical significance is uncertain. Recent mouse experiments, however, show that cross-reactive T cells are capable of mediating protection against ZIKV. In this review, we summarize and discuss the evidence that T cell responses may, at least in part, explain the cross-protection seen against ZIKV from DENV infection, and that T cell antigens should therefore be included in putative Zika vaccines.