Gene mutation has been a concern for researchers because it results in genetic variations with base changes in molecular structure. Researchers continue to explore methods to detect gene mutations, which may help in disease diagnosis, medication guidance, and so on. Currently, the detection methods, such as whole-genome sequencing and polymerase chain reaction, have some limitations in terms of cost and sensitivity. Ligase (an enzyme) can recognize base mismatch as a commonly used tool in genetic engineering. Therefore, the ligase-related nucleic acid amplification technology for detecting gene mutations has become a research hotspot. In this study, the main techniques explored for detecting gene mutations included the ligase detection reaction, ligase chain reaction, rolling circle amplification reaction, enzyme-assisted polymerase chain reaction, and loop-mediated isothermal amplification reaction. This review aimed to analyze the aforementioned techniques and mainly present their advantages and disadvantages, sensitivity, specificity, cost, detection time, applications, and so on. The findings may help develop sufficient grounds for further studies on detecting gene mutations.