Recent advances in observational techniques reveal the widespread exis
tence of magnetic fields in the Universe, and produce much firmer esti
mates of magnetic field strengths in interstellar and intergalactic sp
ace. Ordered, microgauss-level fields are common in spiral galaxy disk
s and halos, and appear to be a common property of the intra-cluster m
edium of clusters of galaxies, indeed well beyond the cluster core reg
ions. Strengths of ordered magnetic fields in the intracluster medium
of cooling flow clusters exceed those which are typical of the interst
ellar medium of the Milky Way, suggesting that galaxy formation, and e
ven 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 fo
r the regeneration of initial seed fields in galaxies, including mecha
nisms of magnetic diffusivity and dissipation which influence field am
plification, are increasingly better, though far from completely, unde
rstood. We review the 'conventional', slow mean field alpha-omega dyna
mo theory for disk galaxies, and more recent modifications to the theo
ry. Fast-acting dynamo mechanisms appear to operate in galaxies, galax
y inflow and outflow, and in cooling flow clusters. Better understandi
ng of the magnetic properties of extragalactic radio jets, including r
ecent 3D numerical simulations, has shown how fast dynamo processes as
sociated with the radio jet/lobe combination can effectivity magnetize
large volumes of intergalactic space. Such processes, and starbust-dr
iven outflow during the galaxy formation epoch, could have produced th
e microgauss level fields now commonly seen in galaxy systems-which wo
uld obviate the need for slow acting dynamos to build up field strengt
h slowly over cosmic time. The observational methods for detecting and
measuring extragalactic magnetic fields are discussed, along with som
e new indirect methods which could be used for inferring field strengt
hs at large redshifts which are otherwise beyond the reach of direct m
easurement. 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 gen
eration 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 gala
xies formed, up to now, largely a 'dark' era.