Diabetes mellitus is a metabolic disorder characterized by chronic hyperglycemia accompanied by the disruption of carbohydrate, lipid, and proteins metabolism and development of long-term microvascular, macrovascular, and neuropathic changes. This review presents the results of spectroscopic studies on the glycation of tissues and cell proteins in organisms with naturally developing and model diabetes and in vitro glycated samples in a wide range of electromagnetic waves, from visible light to terahertz radiation. Experiments on the refractometric measurements of glycated and oxygenated hemoglobin in broad wavelength and temperature ranges using digital holographic microscopy and diffraction tomography are discussed, as well as possible application of these methods in the diabetes diagnostics. It is shown that the development and implementation of multimodal approaches based on a combination of phase diagnostics with other methods is another promising direction in the diabetes diagnostics. The possibilities of using optical clearing agents for monitoring the diffusion of substances in the glycated tissues and blood flow dynamics in the pancreas of animals with induced diabetes have also been analyzed.