Globalization is a very dynamic and complex phenomenon. It exerts a big influence at local, national and regional level through the interconnections between countries, institutions, people, etc. that result in important changes of economic, environmental, political, social and cultural nature. Although globalization is a multidimensional phenomenon, one cannot deny that some of its most visible aspects are of economic nature. The need to measure economic globalization is now of central concern both for academic circles as for the business environment, the mass, specialized mass media and policy makers. Although it is almost impossible to capture such a complex phenomenon in a single representative figure, this paper attempts to place a theoretical debate on more solid scientific basis (in terms of economic globalization indices). In the first part of the paper, we present a brief literature review focusing on some of the different interpretations and beliefs regarding the concept of economic globalization (with reference to the economic literature to date) in order to facilitate future empirical approaches of its impact on national economies. In the second part of the paper, we highlight the extent of the process of economic globalization and the impact on the global economy (and on the Romanian economy), using three indicators quite new in literature: the KOF index of globalization, the globalization index proposed by A.T. Kearney/Foreign Policy and the CSGR Globalization Index. Also we have included in the paper other two important globalization indices – the M-GI and WMRC Index – paying attention to the economic dimension.