The terahertz (THz) region of the electromagnetic spectrum is attracting interest for a broad range of applications ranging from diagnosing electron beams to biological imaging. Most sources of short pulse THz radiation utilize excitation of biased semiconductors or electro-optic crystals by high peak power lasers. For example, this was done by using an un-doped InAs wafer irradiated by a femtosecond free-electron laser (FEL) at the Thomas Jefferson National Accelerator Facility. Microwatt levels of THz radiation were detected when excited with FEL pulses at 1.06 mm wavelength and 10W average power. Recently substantially higher powers of femtosecond THz pulses produced by synchrotron emission were extracted from the electron beamline. Calculations and measurements confirm the production of coherent broadband THz radiation from relativistic electrons with an average power of nearly 20W, a world record in this wavelength range by a factor of 10,000. We describe the source, presenting theoretical calculations and their experimental verification. Potential applications of this exciting new source include driving new non-linear phenomena, performing pump-probe studies of dynamical properties of novel materials, and studying molecular vibrations and rotations, low frequency protein motions, phonons, superconductor band gaps, electronic scattering, collective electronic excitations (e.g., charge density waves), and spintronics.