Abstract: Today econometrics has been widespread applied in empirical study for economic problems. Understanding of econometric methodology is a crucial departure for econometrics. This presentation provided a brief review of modern econometric methodology and its development since 1930s. The core of the review was to show how modern statistical methods, in particular, the modern concept of statistical ‘error’ and ‘probability’ in econometrics, are verified to be scientific, how it provided a scientific method for quantitative analysis of economic phenomena and, how this method more precisely captured the reality. The review also introduced a few new sophistic methods in time series modelling as well as discussed the main issues in current research, aimed at addressing the methodological research in econometric modelling not only is a science but also is an art. Finally, offered my personal thoughts on how econometricians might best be trained in a university, what was we should teach our students and on some issues broadly related to the challenges facing for econometricians in the future.