This paper presents the main trends and the most important challenges related to the use of classical and modern statistical methods in economic research. The first part describes the key changes in quantitative economic and social research, including those related to technological progress. The main features of this evolution are the development of research infrastructure and changes in relations between researchers. The second discusses the need to find a compromise between easily accessible statistical data sets, advanced statistical software to analyse them, and the formal requirements of statistical inference. The third part details the essence and principles of statistical learning and presents a panorama of statistical learning methods. This results in the formulation of a paradigm of statistical learning for conducting modern statistical research.