Replacing the IPv4 protocol with IPv6 on the Internet is currently one of the aims of the European Union policy. The main reason for this replacement is the effeteness of the addresses pool in the IPv4 protocol, which can cause serious complications in the evolution of the Internet and its adaptation in new areas, e.g., in next generation mobile telephony or the so called Internet of Things. Simultaneously, the addressing capabilities of the IPv6 protocol are practically unlimited and its new functionalities increase the attractiveness of its usage. The article discusses the problems connected with the IPv6 deployment on the Internet. Especially, the rules for realization of the IPv6 deployment and rules for cooperation of IPv4 with IPv6 (including cooperation tests) in network infrastructure and in applications are presented. Moreover, the European projects’ results and the activity’s directions of the national project Future Internet Engineering are discussed.