Clustered regularly interspaced short palindromic repeats, CRISPR, has recently emerged as a powerful molecular biosensing tool for nucleic acids and other biomarkers due to its unique properties such as collateral cleavage nature, room temperature reaction conditions, and high target-recognition specificity. Numerous platforms have been developed to leverage the CRISPR assay for ultrasensitive biosensing applications. However, to be considered as a new gold standard, several key challenges for CRISPR molecular biosensing must be addressed. In this paper, we briefly review the history of biosensors, followed by the current status of nucleic acid-based detection methods. We then discuss the current challenges pertaining to CRISPR-based nucleic acid detection, followed by the recent breakthroughs addressing these challenges. We focus upon future advancements required to enable rapid, simple, sensitive, specific, multiplexed, amplification-free, and shelf-stable CRISPR-based molecular biosensors.