  We outline an approach to the inverse problem of Calder\'on that highlights
the role of microlocal normal forms and propagation of singularities and
extends a number of earlier results also in the anisotropic case. The main
result states that from the boundary measurements it is possible to recover
integrals of the unknown coefficient over certain two-dimensional manifolds
called good bicharacteristic leaves. This reduces the Calder\'on problem into
solving a linear integral geometry problem (inversion of a bicharacteristic
leaf transform).
