We present a pedagogical and critical overview of the two-channel Kond
o model and its possible relevance to a number of non-Fermi-liquid all
oys and compounds. We survey the properties of the model, how a magnet
ic two-channel Kondo effect might obtain for Ce3+ ions in metals, and
a quadrupolar Kondo effect for U4+ ions in metals. We suggest that the
incoherent metal behaviour of the two-channel Kondo-lattice model may
be useful in understanding the unusual normal-state resistivity of UB
e13 and speculate that the residual resistivity and entropy of the two
-channel lattice paramagnetic phase might be removed by either antifer
romagnetic (or antiferroquadrupolar) ordering or by a superconducting
transition to an odd-frequency pairing stale.