Address Resolution Protocol
Once a common encapsulation mechanism has been selected for Ethernet, hosts must still convert a 32-bit IP address into a 48-bit Ethernet address. The Address Resolution Protocol (ARP), documented in RFC 826, is used to do this. It has also been adapted for other media, such as FDDI.
ARP works by broadcasting a packet to all hosts attached to an Ethernet. The packet contains the IP address the sender is interested in communicating with. Most hosts ignore the packet. The target machine, recognizing that the IP address in the packet matches its own, returns an answer.
Hosts typically keep a cache of ARP responses, based on the assumption that IP-to-hardware address mapping rarely change.
ARP, Bridging and Routing
ARP is transparent to bridging, since bridging will propagate ARP broadcasts like any other Ethernet broadcast, and will transparently bridge the replies.
A router does not propagate Ethernet broadcasts, because the router is a Network Level device, and Ethernet is a Data Link Level protocol. Therefore, an Internet host must use its routing protocols to select an appropriate router, that can be reached via Ethernet ARPs. After ARPing for the IP address of the router, the packet (targeted at some other Destination Address) is transmitted to the Ethernet address of the router.
Proxy ARP is a technique that can be used by routers to handle traffic between hosts that don't expect to use a router as described above. Probably the most common case of its use would be the gradual subnetting of a larger network. Those hosts not yet converted to the new system would expect to transmit directly to hosts now placed behind a router.
A router using Proxy ARP recognizes ARP requests for hosts on the "other side" of the router that can't reply for themselves. The router answers for those addresses with an ARP reply matching the remote IP address with the router's Ethernet address (in essence, a lie).
Proxy ARP is best thought of as a temporary transition mechanism, and its use should not be encouraged as part of a stable solution. There are a number of potential problems with its use, including the inability of hosts to fall back on alternate routers if a network component fails, and the possibility of race conditions and bizarre traffic patterns if the bridged and routed network segments are not clearly delineated.
Reverse ARP, document in RFC 903, is a fairly simple bootstrapping protocol that allows a workstation to broadcast using its Ethernet address, and expect a server to reply, telling it its IP address.