  Recent progresses in the understanding of the scaling behavior of
self-avoiding flexible polymerized membranes (tethered manifolds) are reviewed.
They rely on a new general renormalization group approach for a class of models
with non-local singular interactions. This approach allows to prove the
existence of a epsilon-expansion for the scaling exponents, and validates the
one loop results obtained by direct renormalization methods. Applications of
the method to polymerized membranes at the tricritical Theta-point are
presented.
