In planetary science, accretion is the process in which solids agglomerate to form larger and larger objects, and eventually planets are produced. The initial conditions are a disc of gas and microscopic solid particles, with a total mass of about 1% of the gas mass. These discs are routinely detected around young stars and are now imaged with the new generation of instruments. Accretion has to be effective and fast. Effective, because the original total mass in solids in the solar protoplanetary disk was probably of the order of ~300 Earth masses, and the mass incorporated into the planets is ~100 Earth masses. Fast, because the cores of the giant planets had to grow to tens of Earth masses to capture massive doses of hydrogen and helium from the disc before the dispersal of the latter, in a few millions of years. The surveys for extrasolar planets have shown that most stars have planets around them. Accretion is therefore not an oddity of the solar system. However, the final planetary systems are very different from each other, and typically very different from the solar system. Observations have shown that more than 50% of the stars have planets that don’t have analogues in the solar system. Therefore the solar system is not the typical specimen. Models of planet accretion have to explain not only how planets form, but also why the outcomes of the accretion history can be so diverse. There is probably not one accretion process but several, depending on the scale at which accretion operates. A first process is the sticking of microscopic dust into larger grains and pebbles. A second process is the formation of an intermediate class of objects called planetesimals. There are still planetesimals left in the solar system. They are the asteroids orbiting between the orbits of Mars and Jupiter, the trans-Neptunian objects in the distant system, and other objects trapped along the orbits of the planets (Trojans) or around the giant planets themselves (irregular satellites). The Oort cloud, source of the long period comets, is also made of planetesimals ejected from the region of formation of the giant planets. A third accretion process has to lead from planetesimals to planets. Actually, several processes can be involved in this step, from collisional coagulation among planetesimals to the accretion of small particles under the effect of gas drag, to giant impacts between protoplanets. Adopting a historical perspective of all these processes provides details of the classic processes investigated in the past decades to those unveiled in the last years. The quest for planet formation is ongoing. Open issues remain, and exciting future developments are expected.