We present a short introduction to a non-standard cosmological scenario motivated by the duality symmetries of string theory, in which the big bang singularity is replaced with a 'big bounce' at high but finite curvature. The bouncing epoch is prepared by a long (possibly infinitely extended) phase of cosmic evolution, starting from an initial state asymptotically approaching the string perturbative vacuum. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'.
Keywords: duality; pre-big bang; string cosmology.