Magnetic flux compression generators offer the largest pulsed power output per unit size or weight when compared with other more conventional systems. They have found widespread use as pulsed power sources for hydrodynamics programs and high magnetic field research at national laboratories or in commercial applications, including exploration for oil and minerals and mine detection. Also, due to their nature as a true one-time-use device with superior energy density, a large portion of applications is defense related. A variety of basic magnetic flux compression generator designs have been developed and tested during the past four decades. All of them rely on the explosive-driven deformation of a system of conductors having an initial, preferably large, inductance. The most successful basic design is the helical flux compression generator, which is capable of producing a high-energy output into large impedance loads, just as it is needed for a practical pulsed power source. This paper will review the advances and state of the art of primarily helical magnetic flux compression generators mainly developed as pulsed power sources and will offer new insights gained as a result of a recently completed five-year AFOSR/DoD Multidisciplinary University Research Initiative program that studied the basic physics and engineering aspects of helical flux compression generators.