  We review the main results of the effective description of the Quantum Hall
fluid for the Jain fillings, nu=m/2pm+1, and the non-standard ones nu=m/pm+2 by
a conformal field theory (CFT) in two dimensions. It is stressed the unifying
character of the m-reduction procedure to construct appropriate twisted CFT
models, called Twisted Models (TM), which by construction reproduce the Quantum
Hall topological properties at those fillings. Indeed for the Jain plateaux we
find that the different descriptions given in the literature fall into
different sectors of the TM for the torus topology. Other interesting aspects
are explicitly seen for the m=2 non standard filling nu=1/p+1 (the pairing
case) as the merging of non-Abelian statistics or the instability of the TM
model (c=2) versus the Moore-Read one (c=3/2). Furthermore by using Boundary
CFT techniques the presence of localized impurities and/or dissipation is shown
to be closely connected with the twisted sector of the TM, whose presence
assures the consistency of the construction and whose role in describing non
trivial global properties of 2D quantum condensed matter systems is still under
study.
