Molecular diagnosis of COVID-19 primarily relies on the detection of RNA of the SARS-CoV-2 virus, the causative infectious agent of the pandemic. Reverse transcription polymerase chain reaction (RT-PCR) enables sensitive detection of specific sequences of genes that encode the RNA dependent RNA polymerase (RdRP), nucleocapsid (N), envelope (E), and spike (S) proteins of the virus. Although RT-PCR tests have been widely used and many alternative assays have been developed, the current testing capacity and availability cannot meet the unprecedented global demands for rapid, reliable, and widely accessible molecular diagnosis. Challenges remain throughout the entire analytical process, from the collection and treatment of specimens to the amplification and detection of viral RNA and the validation of clinical sensitivity and specificity. We highlight the main issues surrounding molecular diagnosis of COVID-19, including false negatives from the detection of viral RNA, temporal variations of viral loads, selection and treatment of specimens, and limiting factors in detecting viral proteins. We discuss critical research needs, such as improvements in RT-PCR, development of alternative nucleic acid amplification techniques, incorporating CRISPR technology for point-of-care (POC) applications, validation of POC tests, and sequencing of viral RNA and its mutations. Improved assays are also needed for environmental surveillance or wastewater-based epidemiology, which gauges infection on the community level through analyses of viral components in the community's wastewater. Public health surveillance benefits from large-scale analyses of antibodies in serum, although the current serological tests do not quantify neutralizing antibodies. Further advances in analytical technology and research through multidisciplinary collaboration will contribute to the development of mitigation strategies, therapeutics, and vaccines. Lessons learned from molecular diagnosis of COVID-19 are valuable for better preparedness in response to other infectious diseases.