Electromagnetic calorimetry forms a key element of almost all current high energy particle physics detectors and has widespread application in related experimental fields such as nuclear physics and astro-particle physics. It will play a particularly important role in the latest generation of experiments at the CERN Large Hadron Collider (LHC), where it is expected that high energy electrons and photons will provide some of the clearest signatures for new discoveries. This article introduces the basic concepts underlying electromagnetic calorimetry and illustrates how these principles have been applied in recent and current detector designs, explaining the connection between technical choices and specific physics goals. Designs are described in sufficient detail to demonstrate the compromises that have to be made in achieving optimum performance within practical constraints. The main emphasis is on the LHC experiments, which provide outstanding examples of the state-of-the-art. Selected examples from other domains, such as nuclear physics and neutrino experiments are also considered and particular attention is given to calorimeter design studies for the proposed International Linear Collider (ILC) where the concept of Particle Flow Analysis is being used as a guiding influence in the overall detector optimization.