Recent advances in observational techniques reveal the widespread existence of magnetic fields in the Universe, and produce much firmer estimates of magnetic field strengths in interstellar and intergalactic space. Ordered, microgauss-level fields are common in spiral galaxy disks and halos, and appear to be a common property of the intra-cluster medium of clusters of galaces, indeed well beyond the cluster core regions. Strengths of ordered magnetic fields in the intracluster medium of cooling flow clusters exceed those which are typical of the interstellar medium of the Milky Way, suggesting that galaxy formation, and even cluster dynamics are, at least in some circumstances influenced by magnetic forces, which also could possibly affect the global dynamics in areas of some galaxies, especially dwarf galaxies, which are rich in interstellar gas and cosmic rays.Physical processes responsible for the regeneration of initial seed fields in galaxies, including mechanisms of magnetic diffusivity and dissipation which influence field amplification, are increasingly better, though far from completely, understood. We review the 'conventional', slow mean field a-w dynamo theory for disk galaxies, and more recent modifications to the theory. Fast-acting dynamo mechanisms appear to operate in galaxies, galaxy inflow and outflow, and in cooling flow clusters. Better understanding of the magnetic properties of extragalactic radio jets, including recent 3~ numerical simulations, has shown how fast dynamo processes associated with the radio jetilobe combination can effec!ivity magnetize large volumes of inlergalactic space. Such processes, and starbust-driven outflow during the galaxy formation epoch, could have produced the microgauss level fields now commonly seen in galaxy systemswhich would obviate the need for slow acting dynamos to build up field strength slowly over cosmic time.The observational methods for detecting and measuring extragalactic magnetic fields are discussed, along with some new indirect methods which could be used for inferring field strengths at large redshifts which are otherwise beyond the reach of direct measurement.Seed fields can be produced in battery-like processes in a variety of systems (stars, supernovae, and supernova winds), and are expelled into intergalactic space. Various cosmological seed field generation mechanisms are reviewed, which could generate seed fields for the subsequently formed galaxies. The question of whether the original seed fields were produced in galaxies, or the pre-recombination early Universe must await a clearer picture of how the first stars and galaxies formed, up to now, largely a 'dark' era.