Abstract: Adaptive filtering algorithms have achieved deep and mature applications across numerous engineering fields owing to their core advantages. Specifically， they require no prior knowledge of signal statistical characteristics and enable real-time adjustment of filtering parameters to adapt to dynamic environments. In communication engineering， they enable channel equalization and signal denoising， effectively counteracting the signal distortion caused by multipath propagation and enhance data transmission reliability. In control engineering， they dynamically compensate for system disturbances and parameter drift， ensuring the stable operation of industrial equipment such as robotic arms and precision machine tools. In radar and sonar systems， they enhance target signal extraction capabilities and reduce false alarm rates in complex electromagnetic and acoustic environments. In biomedical engineering， they play a critical role in noise reduction and feature extraction for weak biological signals， such as electrocardiograms （ECG） and electroencephalograms （EEG）， providing a reliable foundation for disease diagnosis. This paper provides a concise review of the research progress on several common robust adaptive filtering algorithms based on correntropy. The paper covers the following correntropy algorithms： maximum， bias-compensated， complex-valued， geometric-algebraic， and asymmetric correntropy robust algorithms. This paper organizes the research progress of the correntropy algorithms， summarizing the issues encountered and the problems addressed in the literature. Finally， existing challenges and future research directions are discussed for correntropy-robust adaptive filtering algorithms.