Living organisms adapt and function in an ever changing environment. Even under basal conditions they are constantly perturbed by external stimuli. Therefore, biological processes are all non-stationary and highly nonlinear. Thus the study of biomedical processes, which are heavily depending on observations, is crucially dependent on the data analysis. The newly developed method, the Hilbert-Huang Transform (HHT), is ideally suited for nonlinear and non-stationary data analysis such as appeared in the biomedical processes. Different from all other data analysis existing methods, this method is totally adaptive: It derives the basis from the data and based on the data. As a result, it is highly efficient in expanding any time series in their intrinsic modes, which reveal their full physical meaning. In this article, we review biomedical data processing by using HHT. We introduce two exemplary studies: cardiorespiratory synchronization and human ventricular fibrillation. The power and advantages of HHT are apparent from the achievements of these studies.