Over the last decade, several groups of young (mainly low-mass) stars have been discovered in the solar neighbourhood (closer than ~100pc), thanks to cross-correlation between X-ray, optical spectroscopy and kinematic data. These young local associations – including an important fraction whose members are Hipparcos stars – offer insights into the star formation process in low-density environments, shed light on the substellar domain, and could have played an important role in the recent history of the local interstellar medium. Ages estimates for these associations have been derived in the literature by several ways (HR diagram, spectra, Li and Hα widths, expansion motion, etc.). In this work we have studied the kinematic evolution of young local associations and their relation to other young stellar groups and structures in the local interstellar medium, thus casting new light on recent star formation processes in the solar neighbourhood. We compiled the data published in the literature for young local associations, including the astrometric data from the new Hipparcos reduction. Using a realistic Galactic potential we integrated the orbits for these associations and the Sco-Cen complex back in time. Combining these data with the spatial structure of the Local Bubble and the spiral structure of the Galaxy, we propose a recent history of star formation in the solar neighbourhood. We suggest that both the Sco-Cen complex and young local associations originated as a result of the impact of the inner spiral arm shock wave against a giant molecular cloud. The core of the giant molecular cloud formed the Sco-Cen complex, and some small cloudlets in a halo around the giant molecular cloud formed young local associations several million years later. We also propose a supernova in young local associations a few million years ago as the most likely candidate to have reheated the Local Bubble to its present temperature.