  With a brief introduction to one-dimensional channels and conductance
quantisation in mesoscopic systems, we discuss some recent experimental puzzles
in these systems, which include reduction of quantised conductances and an
interesting {\it odd-even} effect in the presence of an in-plane magnetic
field. We then discuss a recent non-homogeneous Luttinger liquid model proposed
by us, which addresses and gives an explanation for the reduced conductances
and the {\it odd-even} effect. We end with a brief summary and discussion of
future projects.
