Terahertz radiation has important prospects in fundamental science and industrial applications, but traditional electronic and optical methods can hardly generate high-power, narrow-band and continuously tunable coherent terahertz radiation at 1-10 THz. Accelerator-based terahertz sources using relativistic ultrashort electron beams or pre-modulated electron bunch trains have the possibility to generate tunable high spectral energy density narrow-band terahertz radiation in the above-mentioned range. This article reviews the recent theoretical and experimental progresses of the Tsinghua University Accelerator Laboratory in accelerator terahertz sources based on relativistic electron beams, as well as the terahertz radiation measurement, beam diagnosis and advanced acceleration technologies developed together with the accelerator terahertz sources.