COVID-19, caused by the SARS-CoV-2 virus, has developed into a global health crisis, causing over 2 million deaths and changing people’s daily life the world over. Current main-stream diagnostic methods in the laboratory include nucleic acid PCR tests and direct viral antigen tests for detecting active infections, and indirect human antibody tests specific to SARS-CoV-2 to detect prior exposure. In this Perspective, we briefly describe the PCR and antigen tests and then focus mainly on existing antibody tests and their limitations including inaccuracies and possible causes of unreliability. False negatives in antibody immunoassays can arise from assay formats, selection of viral antigens and antibody types, diagnostic testing windows, individual variance, and fluctuation in antibody levels. Reasons for false positives in antibody immunoassays mainly involve antibody cross-reactivity from other viruses, as well as autoimmune disease. The spectrum bias has an effect on both the false negatives and false positives. For assay developers, not only improvement of assay formats but also selection of viral antigens and isotopes of human antibodies need to be carefully considered to improve sensitivity and specificity. For clinicians, the factors influencing the accuracy of assays must be kept in mind to test patients using currently imperfect but available tests with smart tactics and realistic interpretation of the test results.