The magnetotropic susceptibility is the thermodynamic coefficient associated with the rotational anisotropy of the free energy in an external magnetic field and is closely related to the magnetic susceptibility. It emerges naturally in frequency-shift measurements of oscillating mechanical cantilevers, which are becoming an increasingly important tool in the quantitative study of the thermodynamics of modern condensed-matter systems. Here we discuss the basic properties of the magnetotropic susceptibility as they relate to the experimental aspects of frequency-shift measurements, as well as to the interpretation of those experiments in terms of the intrinsic properties of the system under study.