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Anycast is defined as a service in IPv6, which provides stateless best effort delivery of an anycast datagram to at least one, and preferably only one host. It is a topic of increasing interest. This paper is an attempt to gather and report on the work done on anycast. There are two main categories at present: network-layer anycast and application-layer anycast. Both involve anycast architectures, routing algorithms, metrics, applications, etc. We also present an efficient algorithm for application-layer anycast, and point out possible research directions based on our research.