Constraint-based multicast routing, which aims at identifying a path that satisfies a set of quality of service (QoS) constraints, has became a very important research issue in the areas of networks and distributed systems. In general, multi-constrained path selection with or without optimization is a NP-complete problem that can not be exactly solved in polynomial time. Hence, accurate constraints-based routing algorithms with a fast running time are scarce, perhaps even non-existent. The expected impact of such a constrained-based routing algorithm has resulted in the proposal of numerous heuristics and a few exact QoS algorithms. This paper aims to give a thorough, concise and fair evaluation of the most important multiple constraint-based QoS multicast routing algorithms known today, and it provides a descriptive overview and simulation results of these multi-constrained routing algorithms. Constraint-based multicast routing, which aims at identifying a path that satisfies a set of quality of service (QoS) constraints, has became a very important research issue in the areas of networks and distributed systems. In general, multi-constrained path selection with or without optimization is a NP-complete problem that can not be precisely solved in polynomial time. Therefore, accurate constraints-based routing algorithms with a fast running time are scarce, perhaps even non-existent. The expected impact of such a constrained-based routing algorithm has resulted in the proposal of numerous heuristics and a few exact QoS algorithms. This paper aims to give a thorough, concise and fair evaluation of the most important multiple constraint-based QoS multicast routing algorithms known today, and it provides a descriptive overview and simulation results of these multi-constrained routing algorithms.