  Experimental studies of the electric and heat currents in the normal,
superconducting and mixed states of high T$_c$ superconductors (HTcS) lead to
characterization, complementary to data obtained from equilibrium property
based techniques. A magnetic field superimposed on the superconducting sample
generates {\it magneto-transport phenomena}, from which an excess electrical
resistivity, an excess thermoelectric power, the Hall or the Nernst effect.
Different behavioral effects allow one to distinguish various dissipation
mechanisms, like quasi particle scattering, vortex motion dissipation and
superconductivity fluctuations, in particular when the Corbino geometry is
used. Moreover bulk measurements of the thermal conductivity and the
electrothermal conductivity in a magnetic field give us sure indications of the
order parameter symmetry. The location of the mixed state phase transition
lines in the technological phase diagram of HTcS are briefly pointed out
through precise measurements performed over broad temperature and magnetic
field ranges. The results are mainly reviewed with the aim of defining further
investigation lines.
