The multi-component signals like speech, vibration, fault, earthquake, heartbeat or electrocardiogram (ECG), brain or electroencephalogram (EEG), and muscles or electromyogram (EMG) etc. show the complex and non-stationary characteristics. The computer- aided automatic system is required for the analysis of such signals in different practical applications. In the computer-based analysis of non-stationary signals, the basic strength lies in the ability of signal processing approach. The traditional signal processing approaches as Fourier transform, short time Fourier transform etc. find limitations for analysis of these signals due to their stationary assumptions for the non-stationary signals. The wavelet transform has gained advancement over traditional methods by the more controlled basis functions. The bases in wavelet transform are also defined from the pre-fixed mother wavelet. The interpretations of non-stationary signals require the adaptive signal processing method. The method has bases which are synchronized with the analyzed signal and able to provide the simplified representation of non-stationary signals for meaningful feature extraction in different applications. The presentation includes the developed adaptive methods for non-stationary signals and possible future directions in the field of adaptive signal processing.