Femtosecond electron beams are novel tool for pump-probe analysis of condensed matter. Progress in developing femtosecond electron beams with the use of both conventional accelerators and laser-plasma accelerators is discussed. In conventional accelerators, the critical issue is timing jitter and drift of the linac-laser synchronization system. Sophisticated electronic devices are developed to reduce the jitter to 330fs (rms); the precise control of temperature at several parts of the accelerator lessens the drift to 1ps (rms). We also report on a full-optical X-ray and e-beam system based on the laser-plasma cathode by using a 12 TW 50fs laser, which enables 40MeV (at maximum), 40fs (cal.), 100pC and quasi-monochromatic single electron bunches. Since the synchronization is done by a passive optical beam-splitter, this system intrinsically has no jitter and drift. It could achieve tens of femtoseconds time-resolved analysis in the near future.