Continuing evolution of the SARS-CoV-2 virus has led to the emergence of many variants, including variants of concern (VOCs). CRISPR-Cas systems have been used to develop techniques for the detection of variants. These techniques focused on the detection of variant-specific mutations in the Spike protein gene of SARS-CoV-2. These sequences mostly carry single-nucleotide mutations and are difficult to differentiate using a single CRISPR-based assay. Here we discuss the specificity of the Cas9, Cas12, and Cas13 systems, important considerations of mutation sites, design of guide RNA, and recent progress in CRISPR-based assays for SARS-CoV-2 variants. Strategies for discriminating single-nucleotide mutations include optimizing the position of mismatches, modifying nucleotides in the guide RNA, and using two guide RNAs to recognize the specific mutation sequence and a conservative sequence. Further research is needed to confront challenges in the detection and differentiation of variants and sublineages of SARS-CoV-2 in clinical diagnostic and point-of-care applications.