Infection with SARS-CoV-2 in humans has caused a pandemic of unprecedented dimensions. SARS-CoV-2 is primarily transmitted through respiratory droplets and targets ciliated epithelial cells in the nasal cavity, trachea, and lungs by utilizing the cellular receptor angiotensin-converting enzyme 2 (ACE2). The innate immune response, including type I and III interferons, inflammatory cytokines (IL-6, TNF-α, IL-1β), innate immune cells (monocytes, DCs, neutrophils, natural killer cells), antibodies (IgG, sIgA, neutralizing antibodies), and adaptive immune cells (B cells, CD8+ and CD4+ T cells) play pivotal roles in mitigating COVID-19 disease. Broad and durable B-cell- and T-cell immunity elicited by infection and vaccination is essential for protection against severe disease, hospitalization and death. However, the emergence of SARS-CoV-2 variants that evade neutralizing antibodies continue to jeopardize vaccine efficacy. In this review, we highlight our understanding the infection- and vaccine-mediated humoral, B and T cell responses, the durability of the immune responses, and how variants continue to threaten the efficacy of SARS-CoV-2 vaccines.