Magnetic hybrid materials are intrinsically heterogeneous in their mechanical properties on different length scales. This gives rise to a number of challenges in the comparison of experimental results to modeling and simulation efforts. This review focused on recent advance on relating the mechanical properties of magnetic hybrid materials to the internal structure of these materials. Special emphasis is given to methods for observing the internal matrix deformations. For 3D and 2D magnetic hybrid materials, we discuss the possibilities and limitations of measuring internal motion and instabilities of the embedded magnetic particles. Although measuring internal matrix deformations in 3D systems is possible, the measurement time for 3D imaging is too long for truly dynamic studies. This limitation can be overcome with 2D imaging in 2D or 3D systems. In all presented systems, measuring the internal deformation also gives the possibility to use the magnetic particles to characterize the mechanical matrix properties locally. The presented experimental advances are put into relation to competing approaches.