Antibody therapeutics and vaccines for coronavirus disease 2019 (COVID-19) have been approved in many countries, with most being developed based on the original strain of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). SARS-CoV-2 has an exceptional ability to mutate under the pressure of host immunity, especially the immune-dominant spike protein of the virus, which is the target of both antibody drugs and vaccines. Given the continuous evolution of the virus and the identification of critical mutation sites, the World Health Organization (WHO) has named 5 variants of concern (VOCs): 4 are previously circulating VOCs, and 1 is currently circulating (Omicron). Due to multiple mutations in the spike protein, the recently emerged Omicron and descendent lineages have been shown to have the strongest ability to evade the neutralizing antibody (NAb) effects of current antibody drugs and vaccines. The development and characterization of broadly neutralizing antibodies (bNAbs) will provide broad strategies for the control of the sophisticated virus SARS-CoV-2. In this review, we describe how the virus evolves to escape NAbs and the potential neutralization mechanisms that associated with bNAbs. We also summarize progress in the development of bNAbs against SARS-CoV-2, human coronaviruses (CoVs) and other emerging pathogens and highlight their scientific and clinical significance.