The VIMOS Public Extragalactic Redshift Survey (VIPERS) is the largest redshift survey ever conducted with the ESO telescopes. It has used the Very Large Telescope to collect nearly 100,000 redshifts from the general galaxy population at 0.5 < z < 1.2. With a combination of volume and high sampling density that is unique for these redshifts, it allows statistical measurements of galaxy clustering and related cosmological quantities to be obtained on an equal footing with classic results from local redshift surveys. At the same time, the simple magnitude-limited selection and the wealth of ancillary photometric data provide a general view of the galaxy population, its physical properties and the relation of the latter to large-scale structure. This paper presents an overview of the galaxy clustering results obtained so far, together with their cosmological implications. Most of these are based on the ∼ 55,000 galaxies forming the first public data release (PDR-1). As of January 2015, observations and data reduction are complete and the final data set of more than 90,000 redshifts is being validated and made ready for the final investigations.