Infectious diseases are a global health problem affecting billions of people. Developing rapid and sensitive diagnostic tools is key for successful patient management and curbing disease spread. Currently available diagnostics are very specific and sensitive but time-consuming and require expensive laboratory settings and well-trained personnel; thus, they are not available in resource-limited areas, for the purposes of large-scale screenings and in case of outbreaks and epidemics. Developing new, rapid, and affordable point-of-care diagnostic assays is urgently needed. This review focuses on CRISPR-based technologies and their perspectives to become platforms for point-of-care nucleic acid detection methods and as deployable diagnostic platforms that could help to identify and curb outbreaks and emerging epidemics. We describe the mechanisms and function of different classes and types of CRISPR-Cas systems, including pros and cons for developing molecular diagnostic tests and applications of each type to detect a wide range of infectious agents. Many Cas proteins (Cas9, Cas12, Cas13, Cas14) have been leveraged to create highly accurate and sensitive diagnostic tools combined with technologies of signal amplification and fluorescent, potentiometric, colorimetric, or lateral flow assay detection. In particular, the most advanced platforms -- SHERLOCK/v2, DETECTR, or CRISPR-Chip -- enable detection of attomolar amounts of pathogenic nucleic acids with specificity comparable to that of PCR but with minimal technical settings. Further developing CRISPR-based diagnostic tools promises to dramatically transform molecular diagnostics, making them easily affordable and accessible virtually anywhere in the world. The burden of socially significant diseases, frequent outbreaks, recent epidemics (MERS, SARS and the ongoing coronoviral nCov-2019 infection) urgently need the developing of express-diagnostic tools. Recently devised CRISPR-technologies represent the unprecedented opportunity to reshape epidemiological surveillance and molecular diagnostics.