The role and importance of mechanical properties of cells and tissues in cellular function, development and disease has widely been acknowledged, however standard techniques currently used to assess them exhibit intrinsic limitations. Recently, Brillouin microscopy, a type of optical elastography, has emerged as a non-destructive, label- and contact-free method that can probe the viscoelastic properties of biological samples with diffraction-limited resolution in 3D. This led to increased attention amongst the biological and medical research communities, but it also sparked debates about the interpretation and relevance of the measured physical quantities. Here, we review this emerging technology by describing the underlying biophysical principles and discussing the interpretation of Brillouin spectra arising from heterogeneous biological matter. We further elaborate on the technique's limitations, as well as its potential for gaining insights in biology, in order to guide interested researchers from various fields.