  Experiments featuring fast heat propagation, or so called "non-local"
transport, were a puzzle for almost two decades. However recently it was shown,
and it is recalled here, that a collective ideal MHD response of the plasma
provides a quantitative agreement with these experiments, whereas transport
plays just a secondary role. Then this work reviews the algebraic approach to
transport data inversion that provides a formally exact solution, as well as a
quantitative assessment of error bars, limited to periodic signals. Conversely,
standard transport reconstructions are shown to sometimes fail to match the
exact solution. The adoption of automated global search algorithms based upon
Genetic Algorithms is bound to greatly increase the probability of finding
optimal solutions. Finally, the standard methods of reconstruction infer the
diffusivity D and pinch V by matching experimental data against those simulated
by transport codes. These methods do not warrant the validity neither of the
underlying models of transport, nor of the reconstructed D(r) and V(r), even
when the results look reasonable.
