The main issues and areas of application of photothermal and optoacoustic spectroscopy are reviewed. Progress in innovative techniques in the most actively developing areas is presented, including microspectroscopy, multispectral techniques, the measurements of single particles and objects with a resolution better than the diffraction limit (nanoscopy) by both optical and probe-based methods. Possible applications of photothermal and optoacoustic spectroscopy for determining the properties of materials, studying photochemistry and fluorescence, chemical reactions, and analytical and applied chemistry, and solving biomedical problems is discussed. Some prospects for the development of these methods are presented.