Effective signal processing methods are essential for machinery fault diagnosis. Most conventional signal processing methods lack adaptability, thus being unable to well extract the embedded meaningful information. Adaptive mode decomposition methods have excellent adaptability and high flexibility in describing arbitrary complicated signals, and are free from the limitations imposed by conventional basis expansion, thus being able to adapt to the signal characteristics, extract rich characteristic information, and therefore reveal the underlying physical nature. This paper presents a systematic and up-to-date review on adaptive mode decomposition in two major topics, i.e., mono-component decomposition algorithms (such as empirical mode composition, local mean decomposition, intrinsic time-scale decomposition, local characteristic scale decomposition, Hilbert vibration decomposition, empirical wavelet transform, variational mode decomposition, nonlinear mode decomposition, and adaptive local iterative filtering) and instantaneous frequency estimation approaches (including Hilbert-transform-based analytic signal, direct quadrature, and normalized Hilbert transform based on empirical AM-FM decomposition, as well as generalized zero-crossing and energy separation) reported in more than 80 representative articles published since 1998. Their fundamental principles, advantages and disadvantages, and applications to signal analysis in machinery fault diagnosis, are examined. Examples are provided to illustrate their performance.