E-Banking has become indispensable and a primary mean of banking in Croatia and the world. The advancment of digital technologies and internet has made the companies go to battle over digital market with their development of digital business and brought them closer to the users. E-Banking has developed so much in the last twenty five years that the classic menas of banking will be obsolete and also with the existing internet and mobile banking, along with the newest E- Bureau, as an offer from E-Banking, other means of E-Banking are constantly being developed and taking their place in the banking market. Internet and mobile banking has changed the way the global economy functions and pushed it towards a new direction and all the companies and private users, which want to keep up with the time, have implemented it in their business and are constantly updating and upgrading it. In this thesis the topic of E-Banking will be discussed on an example of Bank of Zagreb, the emerge of internet banking in Republic of Croatia and in the world and compare the internet and mobile banking. Advantages and disadvantages of internet banking, internet access network and other relevant terms like involvement of digitalisation in certain business processes at larger and smaller banks will be discussed.