With the evolution of generative linguistic steganography techniques, conventional steganalysis falls short in robustly quantifying the alterations induced by steganography, thereby complicating detection. Consequently, the research paradigm has pivoted towards deep-learning-based linguistic steganalysis. This study offers a comprehensive review of existing contributions and evaluates prevailing developmental trajectories. Specifically, we first provided a formalized exposition of the general formulas for linguistic steganalysis, while comparing the differences between this field and the domain of text classification. Subsequently, we classified the existing work into two levels based on vector space mapping and feature extraction models, thereby comparing the research motivations, model advantages, and other details. A comparative analysis of the experiments is conducted to assess the performances. Finally, the challenges faced by this field are discussed, and several directions for future development and key issues that urgently need to be addressed are proposed.