Using semiconductor saturable absorber mirror and diode end-pumping configurations, all solid-state passively mode-locked Nd3+:YVO4 lasers have been successfully developed. The lasers efficiently provide a stable train of ultra-short laser pulses of 12 ps at 1064 nm at the pulse repetition rate adjustable from 8.8 MHz to 100 MHz. The peak power of 1.3 kW and an average laser power of 940 mW were obtained at the pulse repetitive rate of 60 MHz, corresponding to a laser conversion efficiency of 43%. In order to obtain lower pulse repetitive rate and, therefore, higher peak power, a long laser resonator (larger than 15 m) is proposed and successfully developed for diode end-pumped passively mode-locked laser operation using a simple multiple-pass cavity configuration. As a result, the peak laser power up to 5.1 kW was obtained at the pulse repetitive rate of 8.8 MHz. The experimental results of the picosecond laser amplification and the harmonic generations at 532 nm (2nd), 355 nm (3rd) and 266 nm (4th) are presented.