  We review recent measurements of upper (Hc2) and lower (Hc1) critical fields
in clean single crystals of MgB2, and their anisotropies between the two
principal crystallographic directions. Such crystals are far into the "clean
limit" of Type II superconductivity, and indeed for fields applied in the
c-direction, the Ginzburg-Landau parameter k is only about 3, just large enough
for Type II behaviour. Because m0Hc2 is so low, about 3 T for fields in the
c-direction, MgB2 has to be modified for it to become useful for high-current
applications. It should be possible to increase Hc2 by the introduction of
strong electron scattering (but because of the electronic structure and the
double gap that results, the scatterers will have to be chosen carefully). In
addition, pinning defects on a scale of a few nm will have to be engineered in
order to enhance the critical current density at high fields.
