The electromagnetic calorimeter under construction for the CMS experiment at LHC will be the largest crystal calorimeter ever built. The very fast and precise energy measurement of electrons and photons is based upon 76000 lead tungstate crystals read by avalanche photodiodes (APD) in the central barrel region and vacuum phototriodes (VPT) in the endcap regions. The major challenges to be faced are the ability to operate in a strong magnetic field of 4T and under unprecedented radiation levels, the LHC bunch crossing time of 25 ns, the need for a precise energy measurement over a very large dynamic range, from approximately 50 MeV to more than 1 TeV, and the high reliability required of the full on-board readout chain which will be inaccessible after the start of LHC in 2007. A review of the calorimeter design is given and the current status of the construction is reported. Highlights of results obtained during beam tests are also presented.