At certain doping levels, the resistive transitions of cuprate superco
nductors show a parallel shift to lower temperatures under the applica
tion of magnetic fields. This allows a resistive upper critical field
to be defined more easily than for materials such as YBa2Cu3O7, in whi
ch the field broadens the transition. The temperature dependence of th
is field is very unusual, with a steep rise at low temperatures. In th
is paper we review the experimental situation, and discuss the implica
tions of the results far the (H,T) diagram of the cuprates.