In recent years, Internet has known an unprecedented growth, which, in turn, has lead to an increased demand for real-time and multimedia applications that have high Quality-of-Service (QoS) demands. This evolution lead to difficult challenges for the Internet Service Providers (ISPs) to provide good QoS for their clients as well as for the ability to provide differentiated service subscriptions for those clients who are willing to pay more for value added services. Furthermore, a tremendous development of several types of overlay networks have recently emerged in the Internet. Overlay networks can be viewed as networks operating at an inter-domain level. The overlay hosts learn of each other and form loosely-coupled peer relationships. The major advantage of overlay networks is their ability to establish subsidiary topologies on top of the underlying network infrastructure acting as brokers between an application and the required network connectivity. Moreover, new services that cannot be implemented (or are not yet supported) in the existing network infrastructure are much easier to deploy in overlay networks. In this context, multicast overlay services have become a feasible solution for applications and services that need (or benefit from) multicast-based functionality. Nevertheless, multicast overlay networks need to address several issues related to efficient and scalable congestion control schemes to attain a widespread deployment and acceptance from both end-users and various service providers. This report aims at presenting an overview and taxonomy of current solutions proposed that provide congestion control in overlay multicast environments. The report describes several protocols and algorithms that are able to offer a reliable communication paradigm in unicast, multicast as well as multicast overlay environments. Further, several error control techniques and mechanisms operating in these environments are also presented. In addition, this report forms the basis for further research work on reliable and QoS-aware multicast overlay networks. The research work is part of a bigger research project, "Routing in Overlay Networks (ROVER)". The ROVER project was granted in 2006 by EuroNGI Network of Excellence (NoE) to the Dept. of Telecommunication Systems at Blekinge Institute of Technology (BTH).