Satellite systems have the advantage of global coverage and offer a solution for providing broadband access to end users. Local terrestrial networks and terminals can be connected to the rest of the world over Low Earth Orbit (LEO) satellite networks simply by installing small satellite interfaces. With these properties, satellite systems play a crucial role in the global Internet to support real-time and non-real-time applications. Routing in satellite networks, and the integration of satellite networks and the terrestrial Internet are the key issues to support these services. Furthermore, the developments in space technologies enable the realization of deep-space missions such as Mars exploration. The Interplanetary Internet is envisioned to provide communication services for scientific data delivery and navigation services for the explorer spacecrafts and orbiters of future deep-space missions. The unique characteristics posed by deep-space communications call for different research approaches from those in terrestrial networks. The objective of this research is to develop advanced architectures and efficient routing protocols for satellite and space networks to support applications with different traffic types and heterogeneous quality-of-service (QoS) requirements. Specifically, a new QoS-based routing algorithm (QRA) is proposed as a connection-oriented routing scheme to support real-time multimedia applications in satellite networks. Next, the satellite grouping and routing protocol (SGRP) is presented as a unicast routing protocol in a two-layer satellite IP network architecture. The border gateway protocol - satellite version (BGP-S) is then proposed as a unified routing protocol to accomplish the integration of the terrestrial and satellite IP networks at the network layer. Finally, a new routing framework, called the space backbone routing (SBR), is introduced for routing through different autonomous regions in the Interplanetary Internet. SBR provides a self-contained and scalable solution to support different traffic types through the Interplanetary Internet.