Constraint-based routing is an invaluable part of a fullfledged Quality of Service architecture. Unfortunately, QoS routing with multiple additive constraints is known to be a NP-complete problem. Hence, accurate constraint-based routing algorithms with a fast running time are scarce, perhaps even non-existent. The need for such algorithms has resulted in the proposal of numerous heuristics and a few exact solutions. This chapter presents a thorough, concise, and fair evaluation of the most important multi-constrained path selection algorithms known today. A performance evaluation of these algorithms is presented based on a complexity analysis and simulation results. Besides the routing algorithm, dynamic aspects of QoS routing are discussed: how to cope with incomplete or inaccurate topology information and (in)stability issues.