  We know that magnetic fields are pervasive across all scales in the Universe
and over all of cosmic time and yet our understanding of many of the properties
of magnetic fields is still limited. We do not yet know when, where or how the
first magnetic fields in the Universe were formed, nor do we fully understand
their role in fundamental processes such as galaxy formation or cosmic ray
acceleration or how they influence the evolution of astrophysical objects. The
greatest challenge to addressing these issues has been a lack of deep, broad
bandwidth polarimetric data over large areas of the sky. The Square Kilometre
Array will radically improve this situation via an all-sky polarisation survey
that delivers both high quality polarisation imaging in combination with
observations of 7-14 million extragalactic rotation measures. Here we summarise
how this survey will improve our understanding of a range of astrophysical
phenomena on scales from individual Galactic objects to the cosmic web.
