  Chaotic transport is a subject of paramount importance in a variety of
problems in plasma physics, specially those related to anomalous transport and
turbulence. On the other hand, a great deal of information on chaotic transport
can be obtained from simple dynamical systems like two-dimensional
area-preserving (symplectic) maps, where powerful mathematical results like KAM
theory are available. In this work we review recent works on transport barriers
in area-preserving maps, focusing on systems which do not obey the so-called
twist property. For such systems KAM theory no longer holds everywhere and
novel dynamical features show up as non-resistive reconnection, shearless
curves and shearless bifurcations. After presenting some general features using
a standard nontwist mapping, we consider magnetic field line maps for
magnetically confined plasmas in tokamaks.
