Book excerpt: Understanding the magnetic field topology in wire-array Z-pinches is of great significance for their ultimate application to stockpile stewardship and inertial confinement fusion. We have developed and tested several novel techniques involving material-based sensors to measure magnetic fields as a function of space and time in high energy density plasmas on pulsed power machines. We first briefly introduce a technique that was used to measure a lower limit of the maximum magnetic field of a sub-microsecond duration pulse using magnetic reversal in CoPt thin films. The time-varying magnetic field was generated by an exploding wire array plasma called an X pinch produced on the 0.5 MA, 100 ns pulse duration, XP pulsed power generator. We then introduce a technique based on Faraday rotation that was used to measure magnetic fields in wire-array Z-pinches produced on the 1 MA, 100 ns rise time, COBRA pulsed power generator as well as on the XP generator. This technique measures magnetic fields as a function of space and time using Faraday rotation of a single longitudinal mode (SLM) laser through a magneto-optically active bulk waveguide, multicomponent terbium borate glass, placed adjacent to, or within, the wire array. We have measured fields > 10 T with 100 ns rise times outside of a wire-array Z-pinch for the entire duration (~250 ns) of the current pulse and as much as ~2 T inside a wire-array for ~40 ns from the start of current. This is the first time that such rapidly varying and large fields have been measured using the terbium borate glass. The third method, also based on Faraday rotation of SLM laser light utilized an integrated optical fiber sensor (a fiber-sensor-fiber assembly) on the XP pulsed power generator that also yielded a measurement of the magnetic field of a wire-array Z-pinch for part of the current pulse. Finally, we repeated the third method by fabricating a "thin film waveguide" of terbium borate glass to increase the spatial resolution of the measurement. The thin film waveguide was then coupled to an optical fiber system. Although we successfully fabricated thin film nanowaveguides of terbium borate glass, the first time such waveguides have been made, due to poor coupling efficiency of light between components, preliminary Faraday rotation measurements were unsuccessful. The technique developed in this dissertation is potentially viable for magnetic field measurements in high current pulsed power systems if the device is protected from intimate interaction with the high energy density plasma during the time that a magnetic field measurement is to be made.