  The observation of vortices in superconductors was a major breakthrough in
developing the conceptual background for superconducting applications. Each
vortex carries a flux quantum, and the magnetic field radially decreases from
the center. Techniques used to make magnetic field maps, such as magnetic
decoration, give vortex lattice images in a variety of systems. However, strong
type II superconductors allow penetration of the magnetic field over large
distances, of order of the magnetic penetration depth \lambda.
Superconductivity survives up to magnetic fields where, for imaging purposes,
there is nearly no magnetic contrast. Static and dynamic properties of vortices
are largely unknown at such high magnetic fields. Reciprocal space studies
using neutron scattering give insight into the collective behavior. But the
microscopic details of vortex arrangements and their motion remain difficult to
obtain. Direct real space visualization can be made using scanning tunneling
microscopy and spectroscopy (STM/S). Instead of using magnetic contrast, the
electronic density of states describes spatial variations of the quasiparticle
and pair wavefunction properties. These are of order of the superconducting
coherence length \xi, which is much smaller than \lambda. In principle,
individual vortices can be imaged using STM up to the upper critical field
where vortex cores, of size \xi, overlap. In this review, we describe recent
advances in vortex imaging made with scanning tunneling microscopy and
spectroscopy. We introduce the technique and discuss vortex images which reveal
the influence of the Fermi surface distribution of the superconducting gap on
the internal structure of vortices, the collective behavior of the lattice in
different materials and conditions, and the observation of vortex lattice
melting.
