Non-geostationary (NGEO) satellite communication systems are seen as an attractive solution to realize the vision of anywhere, anytime pervasive access to the Internet. Their design and development have thus gained tremendous interest in the last few years. Commencing with a brief overview of general NGEO satellite configurations, this article next addresses the key technical difficulties in the development of NGEO IP-based satellite communications systems. The article discusses routing concerns, mobility management, and transport protocols with an emphasis on TCP performance in NGEO satellite networks. Some key innovations are presented. The Recursive, Explicit, and Fair Window Adjustment (REFWA) scheme is presented as a solution to improve the efficiency and fairness of TCP in NGEO systems. An improvement to the REFWA scheme, REFWA Plus, is also described to combat link errors in satellite environments.