We present our research on the high energy picosecond laser operating at a repetition rate of 1 kHz and the high average power picosecond laser running at 100 kHz based on bulk Nd-doped crystals. With diode-pumped solid state (DPSS) hybrid amplifiers consisting of a picosecond oscillator, a regenerative amplifier, end-pumped single-pass amplifiers, and a side-pumped amplifier, an output energy of 64.8 mJ at a repetition rate of 1 kHz was achieved. An average power of 37.5 W at a repetition rate of 100 kHz pumped by continuous wave laser diodes was obtained. Compact, stable and high power DPSS laser amplifier systems with good beam qualities are excellent picosecond sources for high power optical parametric chirped pulse amplification (OPCPA) and high-efficiency laser processing.