Abstract: ‍ ‍Interference and noise are ubiquitous， which directly affected the performance of signal and information processing in many practical applications， and especially there has a very wide range of needs for weak signal processing， which refers to the target signal of interest with relatively small amplitude corrupted by noise， interference， underwater reverberation or radar clutter. Currently， the theories and methods of weak signal processing are still very difficult and challenging in the field of signal processing. On the one hand， through in-depth research the physical characteristics of weak target signals of interest， it is expected to more explicitly represent the target signal； On the other hand， the latest research progress of applied mathematics and other disciplines is used to improve the theories and methods for weak signal processing， and enhance the ability of target detection and parameter estimation. Moreover， the research work on the above two aspects promotes each other and continues to go ahead. In this paper， the presented methods for weak signal processing are reviewed， which are related to the circuits and systems， the structure of signal， noise and interference， channel and sensors and even multi-sensor array， information fusion and nonlinear technologies， etc. For example， the front-end processing method for the analog data directly measured by different kinds of sensors， correlation processing between the measured and desired signals， Wiener filtering based on the minimum mean square error and its practical implementation i.e.， adaptive noise or interference suppression based on the un-correlation between desired signals and noise/interferences， wavelet transform with milestone significance for signal processing and wide range of applications， subspace based eigen-analysis， sparse representation of feature based on l1-norm for higher accuracy， high-order statistics which is always taken to effectively distinguish the Gaussian and non-Gaussian signals， chaos theory and methods from non-linear dynamic systems， stochastic resonance from bi-stable nonlinear systems， low-rank and sparse decomposition based on the different spatial mathematical structure between the desired signals and interferences， and currently successfully used deep learning. The simulation and experimental results of above methods are illustrated， our research and results on weak underwater acoustic signal processing in recent years are also presented.