Abstract: The formation of the terrestrial planets in the Solar System is normally considered to last several 10s of million years and to have proceeded by giant impacts within a population of Mars-sized protoplanets. Observations of protoplanetary discs around young stars reveal that such discs host several hundred Earth masses of mm-cm sized pebbles. This inspired the pebble accretion theory for planet formation where the cores of giant planets grow by rapid accretion of these pebbles. By extension, pebble accretion should be an important process in terrestrial planet formation as well. I present a series of new papers where we show that Venus, Earth and Mars likely formed within 3-5 Myr by rapid pebble accretion. Volatiles such as water, nitrogen and carbon are delivered by small pebbles that are accreted at the earliest stages of planetary growth. Partition of these volatiles between core, mantle and atmosphere combined with early atmospheric loss gives good matches to the modern atmospheres and water reservoirs of Venus, Earth and Mars. Pebble accretion thus gives a quantitative prediction of volatile budgets and atmospheric compositions of terrestrial planets without invoking stochastic giant impacts as the delivery source.