Since the onset of the COVID-19 pandemic, over 610 million cases have been diagnosed and it has caused over 6.5 million deaths worldwide. The crisis has forced the scientific community to develop tools for disease control and management at a pace never seen before. The control of the pandemic heavily relies in the use of fast and accurate diagnostics, that allow testing at a large scale. The gold standard diagnosis of viral infections is the RT-qPCR. Although it provides consistent and reliable results, it is hampered by its limited throughput and technical requirements. Here, we discuss the main approaches to rapid and point-of-care diagnostics based on RT-qPCR and isothermal amplification diagnostics. We describe the main COVID-19 molecular diagnostic tests approved for self-testing at home or for point-of-care testing and compare the available options. We define the influence of specimen selection and processing, the clinical validation, result readout improvement strategies, the combination with CRISPR-based detection and the diagnostic challenge posed by SARS-CoV-2 variants for different isothermal amplification techniques, with a particular focus on LAMP and recombinase polymerase amplification (RPA). Finally, we try to shed light on the effect the improvement in molecular diagnostics during the COVID-19 pandemic could have in the future of other infectious diseases.