  We study higher spin tensor currents in quantum field theory. Scalar, spinor
and vector fields admit unique "improved" currents of arbitrary spin, traceless
and conserved. Off-criticality as well as at interacting fixed points
conservation is violated and the dimension of the current is anomalous. In
particular, currents J^(s,I) with spin s between 0 and 5 (and a second label I)
appear in the operator product expansion of the stress tensor. The TT OPE is
worked out in detail for free fields; projectors and invariants encoding the
space-time structure are classified. The result is used to write and discuss
the most general OPE for interacting conformal field theories and
off-criticality. Higher spin central charges c_(s,I) with arbitrary s are
defined by higher spin channels of the many-point T-correlators and central
functions interpolating between the UV and IR limits are constructed. We
compute the one-loop values of all c_(s,I) and investigate the RG trajectories
of quantum field theories in the conformal window following our approach. In
particular, we discuss certain phenomena (perturbative and nonperturbative)
that appear to be of interest, like the dynamical removal of the I-degeneracy.
Finally, we address the problem of formulating an action principle for the RG
trajectory connecting pairs of CFT's as a way to go beyond perturbation theory.
