The dynamic development of the Internet definitely affects economic processes on a macro and micro scale. It also changes the face of modern banking. It should be emphasized that in Internet banking and mobile banking we have to deal with completely different security issues compared to traditional banking. In the case of the banking sector, one of the first effects of using the Internet was the creation of a new space for market activity, based on innovative forms of remote distribution of services and contact with customers. At the same time, threats have emerged that violate the security of transactions concluded and deposits held by bank customers. Therefore, discussion of this issue is justified from a social and scientific point of view. This paper discusses the concepts of e-banking, online banking and mobile banking and the threats that exist in these forms of banking. The purpose of this paper is an attempt to analyze the changes taking place in online and mobile banking, taking into account the existing threats in these forms of banking. The following research thesis was adopted : Security is a fundamental condition for the development of online and mobile banking. Recognizing the factors affecting the security of Internet and mobile banking in the financial market is one of the primary responsibilities of the bank and their customers. Security issues definitely affect the development of online and mobile banking. Compared to traditional banking, here we have to deal with much more threats. They cause doubts among customers whether it is safe to use this banking. There are many issues related to security. In this article, the threats related to online banking and mobile banking for individual customers and from banks will be discussed. Security knowledge should be kept up to date and introduced to the public. Banks will be compared using quantitative indicators, such as the number of customers, which determine a bank's position in the financial market.