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Novel routing paradigms based on policies, quality of service (QoS) requirements, and packet content have been proposed for the Internet over the last decade. Constraint-based routing algorithms select a routing path satisfying constraints that are either administrative-oriented (policy routing) or service-oriented (QoS routing). The routes, in addition to satisfying constraints, are selected to reduce costs, balance network load, or increase security. In this article, we discuss several constraint-based routing approaches and explain their requirements, complexity, and recent research proposals. In addition, we illustrate how these approaches can be integrated with Internet label switching and QoS architectures. We also discuss examples of application-level routing techniques used in today's Internet.