Erythrocytes, or red blood cells, transport oxygen to and carbon dioxide from the body's tissues and organs. Red blood cell mechanical properties are altered in a number of diseases such as sickle cell anaemia and malaria. Additionally, mechanically modified red blood cell ghosts are being considered as a long-term, biocompatible carrier for drug delivery and for blood analyte sensing. Brillouin spectroscopy enables viscoelastic characterization of samples at the microscale. In this report, Brillouin spectroscopy is applied to characterize the mechanical properties of red blood cells and red blood cell ghosts.