The potential role for serological tests in the current COVID-19 pandemic has generated very considerable recent interest across many sectors worldwide, inter alia pathologists seeking additional weapons for their armoury of diagnostic tests; epidemiologists seeking tools to gain seroprevalence data that will inform improved models of the spread of disease; research scientists seeking tools to study the natural history of COVID-19 disease; vaccine developers seeking tools to assess vaccine efficacy in clinical trials; and companies and governments seeking tools to aid return-to-work decision-making. However, much of the local debate to date has centred on questions surrounding whether regulatory approval processes are limiting access to serological tests, and has not paused to consider the intrinsically limiting impact of underlying fundamental biology and immunology on where and how different COVID-19 serological tests can usefully be deployed in the response to the current pandemic. We review, from an immunological perspective, recent experimental evidence on the time-dependency of adaptive immune responses following SARS-CoV-2 infection and the impact of this on the sensitivity and specificity of COVID-19 antibody tests made at different time points post infection. We interpret this scientific evidence in terms of mooted clinical applications for current COVID-19 antibody tests in identifying acute infections, in confirming recent or past infections at the individual and population level, and in detecting re-infection and protective immunity. We conclude with guidance on where current COVID-19 antibody tests can make a genuine impact in the pandemic.