  The focus of this paper is on recent progress in muon spin rotation (muSR)
studies of the vortex cores in type-II superconductors. By comparison of muSR
measurements of the vortex core size in a variety of materials with results
from techniques that directly probe electronic states, the effect of
delocalized quasiparticles on the spatial variation of field in a lattice of
interacting vortices has been determined for both single-band and multi-band
superconductors. These studies demonstrate the remarkable accuracy of what some
still consider an exotic technique. In recent years muSR has also been used to
search for magnetism in and around the vortex cores of high-temperature
superconductors. As a local probe muSR is specially suited for detecting static
or quasistatic magnetism having short-range or random spatial correlations. As
discussed in this review, muSR experiments support a generic phase diagram of
competing superconducting and magnetic order parameters, characterized by a
quantum phase transition to a state where the competing order is spatially
nonuniform.
