  This review paper illustrates the main normal and superconducting state
properties of magnesium diboride, a material known since early 1950's, but
recently discovered to be superconductive at a remarkably high critical
temperature Tc=40K for a binary compound. What makes MgB2 so special? Its high
Tc, simple crystal structure, large coherence lengths, high critical current
densities and fields, transparency of grain boundaries to current promises that
MgB2 will be a good material for both large scale applications and electronic
devices. During the last seven month, MgB2 has been fabricated in various
forms, bulk, single crystals, thin films, tapes and wires. The largest critical
current densities >10MA/cm2 and critical fields 40T are achieved for thin
films. The anisotropy ratio inferred from upper critical field measurements is
still to be resolved, a wide range of values being reported, between 1.2 and 9.
Also there is no consensus about the existence of a single anisotropic or
double energy gap. One central issue is whether or not MgB2 represents a new
class of superconductors, being the tip of an iceberg who awaits to be
discovered. Up to date MgB2 holds the record of the highest Tc in its class.
However, the discovery of superconductivity in MgB2 revived the interest in
non-oxides and initiated a search for superconductivity in related materials,
several compounds being already announced to become superconductive: TaB2,
BeB2.75, C-S composites, and the elemental B under pressure.
