Banks under the impact of globalization and digitalization had to change their entire approach to customer relations. The traditional financial sector has undergone important changes due to the rapid development of technologies as well as innovations. Thus, all their traditional services began to be offered online. The research is up-to-date and consists in the fact that, along with the rapidity and efficiency of the operations granted and the services provided by banks, they also involve some risks, both for the bank and for the bank's customers. The purpose of this research is to analyze the transformations and problems faced by banks in the era of digitalization and highlight the conclusions related to this study. The analysis will be carried out by establishing the advantages and disadvantages of digital banking for both the bank and its customers. We aim to highlight the factors that led to the emergence and development of online services both in the world and in the domestic banking sector. The research methods will be analysis, synthesis, induction and deduction. As a result of the research, we propose to empirically analyze different data regarding the degree of digitization of banks in the Republic of Moldova and the problems faced by local banks.