Maxwell's stress tensor is well known from electromagnetic theory. But correct application of it to practical problems is by no means general knowledge even among experts. In this article we present a survey of the electromagnetic stress tensor and of the electromagnetic forces in strongly polarizable materials. We relate the observed ponderomotoric phenomena to the stress tensor and we present a number of applications in modern devices and processes using ferromagnetic colloids, so-called ferrofluids. We emphazise the correct applications of the stress tensor to these examples in contrast to common popular usage of a so-called “electromagnetic pressure”. We predict some new effects, e.g. density variations and pressure measurements in ferrofluids. Our work is based on two preceding articles by the present authors [4, 33] wherein the electromagnetic stress tensor is deduced from conservation laws together with Maxwell's equations and with thermodynamic relations.