With the much-debated exception of the modestly reduced acquisition reported for the RV144 efficacy trial, HIV-1 vaccines have not protected humans against infection, and a vaccine of similar design to that tested in RV144 was not protective in a later trial, HVTN 702. Similar vaccine regimens have also not consistently protected nonhuman primates (NHPs) against viral acquisition. Conversely, experimental vaccines of different designs have protected macaques from viral challenges but then failed to protect humans, while many other HIV-1 vaccine candidates have not protected NHPs. While efficacy varies more in NHPs than humans, vaccines have failed to protect in the most stringent NHP model. Intense investigations have aimed to identify correlates of protection (CoPs), even in the absence of net protection. Unvaccinated animals and humans vary vastly in their susceptibility to infection and in their innate and adaptive responses to the vaccines; hence, merely statistical associations with factors that do not protect are easily found. Systems biological analyses, including artificial intelligence, have identified numerous candidate CoPs but with no clear consistency within or between species. Proposed CoPs sometimes have only tenuous mechanistic connections to immune protection. In contrast, neutralizing antibodies (NAbs) are a central mechanistic CoP for vaccines that succeed against other viruses, including SARS-CoV-2. No HIV-1 vaccine candidate has yet elicited potent and broadly active NAbs in NHPs or humans, but narrow-specificity NAbs against the HIV-1 isolate corresponding to the immunogen do protect against infection by the autologous virus. Here, we analyze why so many HIV-1 vaccines have failed, summarize the outcomes of vaccination in NHPs and humans, and discuss the value and pitfalls of hunting for CoPs other than NAbs. We contrast the failure to find a consistent CoP for HIV-1 vaccines with the identification of NAbs as the principal CoP for SARS-CoV-2.