  Although the effects of interactions in solid state systems still remains a
widely open subject, some limiting cases such as the three dimensional Fermi
liquid or the one-dimensional Luttinger liquid are by now well understood when
one is dealing with interacting electrons in {\it periodic} crystalline
structures. This problem is much more fascinating when periodicity is lacking
as it is the case in {\it quasicrystalline} structures. Here, we discuss the
influence of the interactions in quasicrystals and show, on a controlled
one-dimensional model, that they lead to anomalous transport properties,
intermediate between those of an interacting electron gas in a periodic and in
a disordered potential.
