This thesis presents work on the high average power operation of pulsed diode-pumped solid-state lasers by using a laser configuration known as the bounce geometry. The bounce geometry has previously produced efficient, high power and high spatial quality laser outputs in continuous-wave, Q-switched and modelocked regimes. This thesis explores the capabilities of the bounce geometry for power scaling, shown using Nd:YVO4 and Nd:GdVO4 in both a passively Q-switched laser system and a variety of nonlinear mirror modelocked systems. The high gain experienced by Nd-doped gain media pumped at 808 nm has traditionally posed difficulties in producing stable passive Q-switching with Cr4+:YAG. By using a novel stigmatic design of the bounce geometry that experiences lower gain, but highly circular output, passive Q-switching with > 11 W of average power is produced, at a pulse repetition rate of 190 kHz. This is the highest output power ever achieved from a passively Q-switched Nd-doped vanadate laser to date. Nonlinear mirror modelocking is a passive modelocking technique that employs a χ(2) nonlinear medium in combination with a dichroic output coupler. The first nonlinear mirror modelocking of a bounce geometry laser is presented, obtaining 11.3 W of average power and 57 ps pulse duration using a type-II phase-matched KTP nonlinear crystal. Using type-I phase-matched BiBO, shorter pulses of 5.7 ps in duration are obtained at an average power of 6.1 W. The nonlinear mirror modelocking technique is then applied to the stigmatic bounce geometry laser, obtaining a highly stable train of modelocked pulses with pulse duration 14 ps and an average power of 12 W, with high spatial quality output. Mixed vanadate lasers offer customisation of the laser fluorescence spectrum, but tend to experience lower gain than single vanadates. Using the mixed vanadate combination Nd:Gd0.6Y0.4YVO4 in the bounce geometry, 27.5 W of average power in continuous-wave operation is shown. This is the highest power of any mixed vanadate laser ever reported. By then applying the nonlinear mirror modelocking technique to the mixed vanadate system, 16.8 W of average modelocked output power and a pulse duration of 12.7 ps is obtained. This is simultaneously the first time that the nonlinear mirror technique has been applied to mixed vanadate gain media and the highest power of any modelocked mixed vanadate laser to date. Finally, power scaling of a nonlinear mirror modelocked Nd:GdVO4 laser in the bounce geometry is achieved through use of the double bounce geometry design and through use of a high power pump diode. The system employing the high power pumping produced > 30 W of average power — world record power using the nonlinear mirror technique.