New THz radiation devices made of high-Tc superconductors are fabricated and their characteristics are studied in detail. Ultrashort electromagnetic pulses with 0.5 ps width have been radiated into free space from current biased devices made of superconducting YBa2Cu3O7 (YBCO) films by exciting with femtosecond laser pulses. The Fourier spectrum of them extends up to 3 THz. The radiation mechanism is ascribed to the ultrafast supercurrent modulation by the optical pulses. The THz waveform is analyzed using rate equations describing the relaxation of photoexcited quasiparticles. By the improvement of the device structure and the collecting optics, the radiation power can be increased up to 0.5 µW. A new type THz radiation from YBCO films under an external magnetic field without a transport current is also reported.