We describe three specific high power laser systems that are being developed in our laboratory for many applications in high field science, nonlinear optics and material processing. We report on a femtosecond petawatt-class Ti:sapphire chirped-pulse amplification laser system that can produce a pulse energy of 20 J of 40 fs pulse duration, a picosecond high intensity Yb:YAG chirped-pulse amplification laser system that can generate a pulse energy of 100 mJ of 0.5 ps pulse duration, and a nanosecond high repetition rate Nd:YAG laser system that can provide an average power of 360 W with a pulse duration of 30 ns delivered at a 1 kHz repetition rate. We discuss the basic design aspects and present the results from our experimental investigations of these laser systems.