  We review the current theoretical understanding how growth from micro-meter
sized dust to massive giant planets occurs in disks around young stars. After
introducing a number of observational constraints from the solar system, from
observed protoplanetary disks, and from the extrasolar planets, we simplify the
problem by dividing it into a number of discrete stages which are assumed to
occur in a sequential way. In the first stage - the growth from dust to
kilometer sized planetesimals - the aerodynamics of the bodies are of central
importance. We discuss both a purely coagulative growth mode, as well as a
gravoturbulent mode involving a gravitational instability of the dust. In the
next stage, planetesimals grow to protoplanets of roughly 1000 km in size.
Gravity is now the dominant force. The mass accretion can be strongly
non-linear, leading to the detachment of a few big bodies from the remaining
planetesimals. In the outer planetary system (outside a few AU), some of these
bodies can become so massive that they eventually accrete a large gaseous
envelope. This is the stage of giant planet formation, as understood within the
core accretion-gas capture paradigm. We also discuss the direct gravitational
collapse model where giant planets are thought to form directly via a
gravitational fragmentation of the gas disk. In the inner system, protoplanets
collide in the last stage - probably after the dispersal of the gaseous disk -
in giant impacts until the separations between the remaining terrestrial
planets become large enough to allow long term stability. We finish the review
with some selected questions.
