  We review a systematic many-body method capable of describing Fermi liquid
and Non-Fermi liquid behavior of quantum impurity models at low temperatures on
the same footing. The crossover to the high temperature local moment regime is
covered as well. The approach makes use of a pseudo-particle representation of
the impurity Hilbert space in the limit of infinite Coulomb repulsion $U$ as
well as for finite $U$. Approximations are derived from a generating
Luttinger-Ward functional, in terms of renormalized perturbation theory in the
hybridization $V$. Within a ``conserving T-matrix approximation'' (CTMA),
including all two-particle vertex functions, an infinite series of leading
infrared singular skeleton diagrams is included. The local constraint is
strictly enforced. Applied to the SU(N) $\times$ SU(M) multichannel Anderson
model the method allows to recover the Fermi liquid behavior of the single
channel case, as well as the non-Fermi liquid behavior in the multi-channel
case. The results are compared with the ``non-crossing approximation'' (NCA)
and with data obtained by the numerical renormalization group and the Bethe
ansatz. The generalization of the method to the case of finite on-site
repulsion $U$ is presented in a systematical way and solved on the level of a
generalized NCA, fully symmetric with respect to all virtual excitations of the
model.
