The COVID-19 pandemic is an ongoing global pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in 2020–2021. COVID-19 is becoming one of the most fatal pandemics in history and brings a huge challenge to the global healthcare system. Opportune detection, confinement, and early treatment of infected cases present the first step in combating COVID-19. Diagnosis via viral nucleic acid amplification tests (NAATs) is frequently employed and considered the standard procedure. However, with an increasing urge for point-of-care tests, rapid and cheaper immunoassays are widely utilized, such as lateral flow immunoassay (LFIA), which can be used for rapid, early, and large-scale detection of SARS-CoV-2 infection. In this narrative review, the principle and technique of LFIA applied in COVID-19 antigen and antibody detection are introduced. The diagnostic sensitivity and specificity of the commercial LFIA tests are outlined and compared. Generally, LFIA antigen tests for SARS-CoV-2 are less sensitive than viral NAATs, the “gold standard” for clinical COVID-19 diagnosis. However, antigen tests can be used for rapid and mass testing in high-risk congregate housing to quickly identify people with COVID-19, implementing infection prevention and control measures, thus preventing transmission. LFIA anti-SARS-CoV-2 antibody tests, IgM and/or IgG, known as serology tests, are used for identification if a person has previously been exposed to the virus or vaccine immunization. Notably, advanced techniques, such as LFT-based CRISPR-Cas9 and surface-enhanced Raman spectroscopy (SERS), have added new dimensions to the COVID-19 diagnosis and are also discussed in this review.