The use of new types of intelligent materials is becoming increasingly widespread. These include magnetoactive elastomers with hard magnetic filling components, which offer the unique chance to adapt active and passive material properties. In this context, this paper presents an overview of the experimental results on the study of the magnetic properties of elastic composites with a magnetic hard component. First-order reversal curves, which are recorded with a vibrating sample magnetometer, are used as method to characterize the magnetic material behavior. The influence of various parameters on the process of magnetization of composites is considered, including the stiffness of the polydimethylsiloxane-based matrix polymer, the particle ratio and the particle size as well as the so-called training effect.