  In this paper we review recent theoretical results for transport in a
one-dimensional (1d) Luttinger liquid. For simplicity, we ignore electron spin,
and focus exclusively on the case of a single-mode. Moreover, we consider only
the effects of a single (or perhaps several) spatially localized impurities.
Even with these restrictions, the predicted behavior is very rich, and
strikingly different than for a 1d non-interacting electron gas. The method of
bosonization is reviewed, with an emphasis on physical motivation, rather than
mathematical rigor. Transport through a single impurity is reviewed from
several different perspectives, as a pinned strongly interacting ``Wigner"
crystal and in the limit of weak interactions. The existence of fractionally
charged quasiparticles is also revealed. Inter-edge tunnelling in the quantum
Hall effect, and charge fluctuations in a quantum dot under the conditions of
Coulomb blockade are considered as examples of the developed techniques.
