Planets form in protoplanetary discs around young stars as dust and ice particles collide to form larger and larger bodies. I will present a coherent theory framework for the formation of planetary systems, based on the storyline in our recent Annual Reviews paper (Johansen & Lambrechts, 2017). Dust grows to pebbles by coagulation and deposition of volatile ices, but the continued growth to planetesimals is hampered by the poor sticking of mm-cm-sized pebbles. Planetesimals can nevertheless form by gravitational collapse of pebble clumps concentrated in the turbulent gas through the streaming instability. The subsequent growth initially occurs by planetesimal-planetesimal collisions, but the accretion rate of pebbles dominates the growth from 1000-km-sized protoplanets to form terrestrial planets and the solid cores of gas giants, ice giants and super-Earths.