CW diode pumped solid state lasers have sought for various scientific, medical and military applications, where compact reliable, stable, and highly efficient sources are desirable. There are several applications such as fiber- optic sensing or range finding which require short bursts of high peak power densities at multi-kilohertz repetition rates, and with a good beam quality. An extensive research on the properties of passively Q-switched, CW diode-pumped, ND-lasers has been conducted. We have used various pumping schemes to diode pump the Q-switched Nd:YAG and Nd:YVO4 laser crystals. Such schemes are transverse pumping by a cylindrical microlens-coupled diode array or longitudinally pumping by a fiber-coupled diode array. The passive Q- switching elements were Cr4+:YAG (polished, uncoated) and Cr4+:GGG (polished, coated), which were inserted inside the laser resonator. The 1.06 micrometers laser emission shows a repetitive modulation in the kHz frequency domain, and temporal bandwidth, full width at half maximum, in the range of 50 - 600 nsec. The modulation frequency and bandwidth depend on the characteristics of the Q-switching material (e.g. Cr4+ concentration, sample thickness) and on the input power level of the diode array used. We shall report design parameters and performance of various types of passively Q-switched and free-running diode pumped Nd-lasers. We shall present and discuss methods to increase the efficiency of Q-switched solid state lasers.