In 2018, the researchers from the Massachusetts Institute of Technology, inspired by the neural network of Caenorhabditis elegans, proposed the liquid neural network (LNN). This type of neural network more closely resembles the thinking patterns of the human brain and can process sequential tasks more efficiently. This study introduces and analyzes research related to LNN. It primarily summarizes the principal models of LNN, highlighting their distinctions from and connections to simple recurrent neural network (Simple RNN), long short-term memory (LSTM) network, and time-constant recurrent neural network (TC-RNN), as well as the advantages that LNN possesses over TC-RNN. Furthermore, it details the applications of LNN in autonomous driving, drone navigation, and stock prediction, analyzing the specific LNN models employed in these areas. Finally, the study summarizes the challenges faced and discusses the prospects for future development.