Planets form in gaseous discs around young stars as dust and ice particles collide and grow to ever larger bodies. The formation of km-sized planetesimals from smaller cm-dm sized particles faces major difficulties in the traditional coagulation scenario. Such particles do not stick well and very quickly drift towards the star to sublimate in the inner nebula. I will present an alternative scenario where overdense regions of particles collapse under their own gravity to form massive 1000-km-scale planetesimals. The overdensities are seeded by hydrodynamical streaming instabilities arising in the coupled motion of gas and particles. I will also present new results showing that very large planetesimals can continue to accrete pebbles extremely efficiently. Formation of gas-giant cores by pebble accretion is 1,000-10,000 times faster than traditional core formation by run-away planetesimal accretion, explaining the presence of giant planets in the solar system as well as extrasolar planets observed to orbit very far from their host star.