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Solid state theory, density functional theory and its generalizations forcorrelated systems together with numerical simulations on supercomputers allownowadays to model magnetic systems realistically and in detail and can be evenused to predict new materials, paving the way for more rapid materialdevelopment for applications in energy storage and conversion, informationtechnologies, sensors, actuators etc. Modelling magnets on different lengthscales (between a few \r{A}ngstr\"om and several micrometers) requires,however, approaches with very different mathematical formulations. Parametersdefining the material in each formulation can be determined either by fittingexperimental data or from theoretical calculations and there exists awell-established approach for obtaining model parameters for each length scaleusing the information from the smaller length scale. In this review, thisapproach will be explained step-by-step in textbook style with examples ofsuccessful multiscale modelling of different classes of magnetic materials fromthe research literature as well as based on results newly obtained for thisreview.

From electronic structure to magnetism and skyrmions (Topical review)