This paper describes the embedded block coding algorithm at the heart of the JPEG2000 image compression standard. The paper discusses key considerations which led to the development and adoption of this algorithm, and also investigates performance and complexity issues. The JPEG2000 coding system achieves excellent compression performance, somewhat higher (and, in some cases, substantially higher) than that of SPIHT with arithmetic coding, a popular benchmark for comparison. The algorithm utilizes the same low complexity binary arithmetic coding engine as JBIG2. Together with careful design of the bit-plane coding primitives, this enables comparable execution speed to that observed with the simpler variant of SPIHT without arithmetic coding. The coder offers additional advantages including memory locality, spatial random access and ease of geometric manipulation. 36 Pages