  We describe some recent results concerning the statistical properties of a
self-interacting polymer stretched by an external force. We concentrate mainly
on the cases of purely attractive or purely repulsive self-interactions, but
our results are stable under suitable small perturbations of these pure cases.
We provide in particular a precise description of the stretched phase (local
limit theorems for the end-point and local observables, invariance principle,
microscopic structure). Our results also characterize precisely the
(non-trivial, direction-dependent) critical force needed to trigger the
collapsed/stretched phase transition in the attractive case. We also describe
some recent progress: first, the determination of the order of the phase
transition in the attractive case; second, a proof that a semi-directed polymer
in quenched random environment is diffusive in dimensions 4 and higher when the
temperature is high enough. In addition, we correct an incomplete argument from
one of our earlier works.
