In modern world, the development of Internet and information technology has a major influence on the development of commerce. Advantages of the electronic way of trade come with the cut of business costs, shorter delivery time, larger offer of goods and services as well as a shorter time between payment and takeover of goods and services. The number of Internet users is growing every day and the growth of information technologies has enabled a more sophisticated trade process. Banking information technologies have been developed simultaneously with the development of the Internet and Internet technology, as banks have recognized the enormous potential that technology provides for their work. This final paper will describe how modern information technology is being applied in the banking system. Today, banks are doing less and less of their business in a traditional way, through branch banks, and they increasingly use new distribution channels to interact with customers. Throughout the paper, new technologies will be explained. New technologies enable a large number of services that people would normally have to stand in lines for at branch banks. First, Internet and mobile banking are explained. The development of Internet technology in the world also reflects on Croatia. Statistics show that there is an increasing number of Internet and mobile banking users. Although modern banking has an increasing number of satisfied customers due to its many advantages, it also faces challenges such as security. The possibilities of using mobile banking are detailed through the example of Zagrebačka banka, one of the leading banks in Croatia in the field of innovation. Through the research of the topic it is obvious that traditional banking has undergone a serious transformation in just a few years and that there is an increasing number of users, but there will always be a need for human work in the business of modern banking systems, primarily in the area of data protection, and prevention of their abuse at the expense of the user.