This thesis explains in more details the concepts of internet forms of payment, mobile forms of payment, digital currencies and cryptocurrencies. Before in-depth research and analysis of the main topics, it will be necessary to explain the history and implementation of internet and mobile payment systems and their main characteristics. The main focus of the thesis will be on mobile forms of payment with explanation of the way they work, their availability in the world and in the Republic of Croatia, especially about Apple Pay mobile payment system. It will be researched in detail how does it function, its security and its implementation in the world and the Republic of Croatia. Its competitor in the global, at the same time Croatian market - Google Pay - will also be studied. In addition to mobile payment systems, the thesis will also be based on digital currencies, their theory and way of working with a focus on the subtype of the same - cryptocurrencies. The system of cryptocurrency functionality will be explained in detail with the example of the first and most popular cryptocurrency - Bitcoin. In addition to Bitcoin, alternative cryptocurrencies will be explained, as well as the possibility and implementation of all cryptocurrencies in the real world. Finally, an analysis of research on the use of online forms of payment and cryptocurrencies in the Republic of Croatia was conducted in order to see the current and realistic picture of Internet and mobile payment systems and cryptocurrencies in the Republic of Croatia. It could be concluded that internet and mobile payment systems are quite common in the Croatian market, that they are used and that the public's awareness of digital currencies and cryptocurrencies is very high, but so is skepticism about them.