The adaptive decomposition algorithm is a powerful tool for signal analysis, because it can decompose signals into several narrow-band components, which is advantageous to quantitatively evaluate signal characteristics. In this paper, we present a comparative study of four kinds of adaptive decomposition algorithms, including some algorithms deriving from empirical mode decomposition (EMD), empirical wavelet transform (EWT), variational mode decomposition (VMD) and Vold–Kalman filter order tracking (VKF_OT). Their principles, advantages and disadvantages, and improvements and applications to signal analyses in dynamic analysis of mechanical system and machinery fault diagnosis are showed. Examples are provided to illustrate important influence performance factors and improvements of these algorithms. Finally, we summarize applicable scopes, inapplicable scopes and some further works of these methods in respect of precise filters and rough filters. It is hoped that the paper can provide a valuable reference for application and improvement of these methods in signal processing.