Electron beam based radiation sources provide electromagnetic radiation for countless applications. The properties of the radiation are primarily determined by the properties of the electron beam. Compact laser driven accelerators are being developed that can provide ultrashort electron bunches (femtosecond duration) with relativistic energies reaching toward a GeV. The electron bunches are produced when an intense laser interacts with a dense plasma and excites a large amplitude plasma density modulation (wakefield) that can trap background electrons and accelerate them to high energies. The short-pulse nature of the accelerated bunches and high particle energy offer the possibility of generating radiation from one compact source that ranges from coherent terahertz to gamma rays. The intrinsic synchronization to a laser pulse and unique character of the radiation offer a wide range of possibilities for scientific applications. Two particular radiation source regimes are discussed: coherent terahertz emission, and X-ray emission based on betatron oscillations and Thomson scattering.