Multicast has become an important service in modern network applicatio
ns. Multicast routing is a difficult issue, particularly under delay o
r bandwidth constraints. This paper discusses Steiner trees in the mod
eling of multicast routings and various routing constraints required b
y applications. It also discusses the existing multicast routing algor
ithms, especially the routings under constraints, such as delay constr
aint, limited available bandwidth, and traffic load balancing. Extensi
ve simulations have been conducted to reveal the relationships between
the network cost of the routing and each of the discussed constraints
.