The markets for network-based products and services pose particular problems with regard to competition. The transition from monopolistic to competitive structures and the issues of infrastructure sharing, dominant players and network externalities have all been subject to intensive debates. Despite liberalisation, deregulation and privatisation - and the quasiautomatic solutions they seemed to present - a number of problems persist. Furthermore, the regulation which was introduced as a remedy for distortions of competition during the period of transition from monopoly to competition has not ended with market liberalisation. Each new generation of network technologies creates new challenges to be addressed by regulators and competition authorities, and each industry presents specific problems. The following article discuss a number of the persisting and new questions concerning competition in selected network-based industries.