Nowadays, when discussing banking, we can not neglect new technologies such as internet banking. The internet banking provides competitive advantage to banks. Internet banking became a need for customers and they demand this facility when they open an account. This paper explains the technology acceptance model and the customer behaviour regarding this innovation system called internet banking. Moreover, the role of this tool is highlighted by the authors. Based on case studies, the paper reveals the importance of this new trend in banking. Technology, finance and customer created this new technology that became a need for everyone of us. The internet banking, using a personal computer or any intelegent device brings the customer closer to the its financial provider. We can talk about customer relationship management by using this new tool and also gaining customer trust and loyality. Future trends in Internet banking and growing the number of users are discussed in the below paper.