Loop quantum cosmology is a non-perturbative canonical quantization of simple cosmological models based on loop quantum gravity. In recent years, a greater control on the underlying quantum theory has revealed a picture where the big bang is replaced by a quantum bounce at Planck scale. The evolution across the bounce is unitary and non-singular without a need of choice of exotic potential or matter. By analysis of an exactly solvable model of a homogeneous and isotropic spacetime we will describe how the backward evolution of our universe with the quantum constraint leads to a pre big bang branch. We will also discuss the way it predicts modifications to Friedman dynamics at high curvatures, contrasts with the Wheeler-DeWitt scenario and semi-classicality across the bounce.