The embedded security community has been looking at the ECC ever since it was introduced. Hardware designers are now challenged by limited area (15k Gates), low power budget (100uw) and sophisticated physical attacks. This talk will report the state-of-the-art ECC implementations for ultra-constrained devices. We take a passive RFID tag as our potential target. We will discuss the known techniques to realize ECC on such kind of devices, and what are the challenges we face now and in the near future.