  Critical phenomena emerging from the critical end point of a first-order
transition are ubiquitous in nature. Here we bring the concept of a
supercritical crossover, the Widom line, initially developed in the context of
fluids, into the interacting matter described by quantum chromodynamics (QCD).
We show that the existence of the putative critical end point between hadron
gas and quark-gluon plasma in the temperature versus chemical potential of the
QCD phase diagram implies the existence of a Widom line emerging from it in the
supercritical region. We survey the thermodynamic anomalies already identified
in simplified theoretical models of QCD exhibiting a critical end point, to
show that they can be interpreted in terms of a Widom line. Then we suggest
possible directions where the Widom line concept could provide new light on the
QCD phase diagram.
