Vibration-based condition monitoring and fault diagnosis are becoming more common in the industry to increase machine availability and reliability. Considerable research efforts have recently been directed towards the development of adaptive signal processing methods for fault diagnosis. Two adaptive signal decomposition methods, i.e. the empirical mode decomposition (EMD) and the local mean decomposition (LMD), are widely used. This chapter is intended to summarize the recent developments mostly based on the authors' works. It aims to provide a valuable reference for readers on the processing and analysis of vibration signals collected from rotating machinery.