Covalent organic frameworks (COFs) have emerged as highly crystalline porous organic materials and proven to be potential candidates for various interesting applications, such as gas adsorption and separation, catalysis, energy storage, and sensing. Fluorescence-based sensing has attracted significant attention due to its high selectivity, rapid response time, and real-time monitoring. Lately, luminescent COFs have been developed as sensing probes to detect various target molecules. In this review, we present a comprehensive account of the chronological development of the field of COFs starting from 2005 to date. We describe the design principles of COFs with a focus on various topologies reported, classification of their structural diversity based on thirty-two linkages and dimensionality, methods for their synthesis with examples, and the use of various characterization techniques. Interestingly, almost half of the COFs contain nitrogen-rich linkages. With a background in different processes involved in fluorescence sensing, we illustrate the potential applicability of nitrogen-rich COFs as sensors for numerous analytes, such as explosives, volatile organic molecules, pH, temperature, toxic anions, metal ions and biomolecules in different media utilizing their striking features with predesigned structures and diverse functionality.