  Solid state theory, density functional theory and its generalizations for
correlated systems together with numerical simulations on supercomputers allow
nowadays to model magnetic systems realistically and in detail and can be even
used to predict new materials, paving the way for more rapid material
development for applications in energy storage and conversion, information
technologies, sensors, actuators etc. Modelling magnets on different length
scales (between a few \r{A}ngstr\"om and several micrometers) requires,
however, approaches with very different mathematical formulations. Parameters
defining the material in each formulation can be determined either by fitting
experimental data or from theoretical calculations and there exists a
well-established approach for obtaining model parameters for each length scale
using the information from the smaller length scale. In this review, this
approach will be explained step-by-step in textbook style with examples of
successful multiscale modelling of different classes of magnetic materials from
the research literature as well as based on results newly obtained for this
review.
