Multicasting is an efficient communication mechanism for group-oriented applications such as videoconferencing, broadcasting stock quotes, interactive group games, and video on demand. The lack of security obstructs a large deployment of this efficient communication model. This limitation motivated a host of research works that have addressed the many issues relating to securing the multicast, such as confidentiality, authentication, non-repudiation, integrity, and access control. Many applications, such as broadcasting stock quotes and video-conferencing, require data origin authentication of the received traffic. Hence, data origin authentication is an important component in the multicast security architecture. Multicast data origin authentication must take into consideration the scalability and the efficiency of the underlying cryptographic schemes and mechanisms, because multicast groups can be very large and the exchanged data is likely to be heavy in volume (streaming). Besides, multicast data origin authentication must be robust enough against packet loss because most multicast multimedia applications do not use reliable packet delivery. Therefore, multicast data origin authentication is subject to many concurrent and competitive challenges, when considering these miscellaneous application-level requirements and features. In this article we review and classify recent works dealing with the data origin authentication problem in group communication, and we discuss and compare them with respect to some relevant performance criteria.