  Despite the increase in observational data on exoplanets, the processes that
lead to the formation of planets are still not well understood. But thanks to
the high number of known exoplanets, it is now possible to look at them as a
population that puts statistical constraints on theoretical models. A method
that uses these constraints is planetary population synthesis. Its key element
is a global model of planet formation and evolution that directly predicts
observable planetary properties based on properties of the natal protoplanetary
disk. To do so, global models build on many specialized models that address one
specific physical process. We thoroughly review the physics of the sub-models
included in global formation models. The sub-models can be classified as models
describing the protoplanetary disk (gas and solids), the (proto)planet (solid
core, gaseous envelope, and atmosphere), and finally the interactions
(migration and N-body interaction). We compare the approaches in different
global models and identify physical processes that require improved
descriptions in future. We then address important results of population
synthesis like the planetary mass function or the mass-radius relation. In
these results, the global effects of physical mechanisms occurring during
planet formation and evolution become apparent, and specialized models
describing them can be put to the observational test. Due to their nature as
meta models, global models depend on the development of the field of planet
formation theory as a whole. Because there are important uncertainties in this
theory, it is likely that global models will in future undergo significant
modifications. Despite this, they can already now yield many testable
predictions. With future global models addressing the geophysical
characteristics, it should eventually become possible to make predictions about
the habitability of planets.
