Abstract: Analyzing data from real world is a challenge; we have to face the limitations imposed by reality: nonstationarity, nonlinearity and the availability of information.  Traditional methods, strictly adhesive to rigorous mathematical rules, cannot fully circumvent these restrictions.  As a result, data analysis is reduced to merely data processing, and truth remains concealed.  Many of the difficulties could actually be traced back to the lack of correct definition for frequency, a critical physical quantity.  In fact, once the frequency can be properly extracted from the data, many difficulties such as quantification of degree of nonlinearity and nonstationarity could be achieved easily.  Furthermore, the elusive definition and determination of the trend of a given data set can also be accomplished.   The adaptive HHT, consisted of Empirical Mode Decomposition (EMD) and the Hilbert Spectral Analysis (HSA) methods, offer an attractive possibility.  Many new advances in HHT are made in recent years that including the Nonlinear Matching Pursuit method, Ensemble Empirical Mode Decomposition (EEMD), Instantaneous Frequency computations, Trend determination, Time-dependent Intrinsic Correlation (TIDC), density representation of Hilbert Spectrum, and the extension of the time series analysis method to multi-dimensional data.  Although these advances have made the HHT method much more robust and mature, many mathematical problems remain to be resolved.  It is hoped that this introduction would not only accentuate applications, but also call upon the mathematical community to work on adaptive data analysis in general and the HHT in particular, so that we can establish Data Analysis as a valid and integral part of scientific pursue rather than a subservient detachment of a research team.