The Fourth Industrial Revolution or Industry 4.0 refers, in simple terms, to the way in which the technologies like artificial intelligence, autonomous vehicles, augmented reality and the internet of things are merging with the physical life of the people all around the globe. This new “era” is expected to transform the economies, employment and even the society in which we live today in a revolutionary way. The digital economy is very different in comparison to the traditional one and it is the result of the accelerated evolution of telecommunications, internet and electronics, and their integration in our everyday life. This arising economy is favoring the development of a new type of business, i.e. e-business. The process of the transformation of the actual economy in a digital one needs a set of favorable factors and a period of time, named period of transition. In this context, it is necessary to understand and to assess how advanced the transition process is in each EU country so that to be able to create and implement the suitable strategies who will lead to the digital economy. At EU level it was create an index - Digital Economy and Society Index (DESI) – with the aim to measure the progress of EU countries towards a digital economy and society. Our paper presents this index and make a comparative analysis of its evolution during the last 5 years. The results show an intens preoccupation of all EU countries for the improvement of the sectors considered in the calculation of DESI and the progress made by some states in this field.