Spectroscopy of organic molecular glasses and cold-deposited films is reviewed. The emphasis is on demonstration of the capabilities of such Spectroscopy in tackling the fundamental problems in the physics of the amorphous state. It is shown that in discussing the structural properties a considerable amount of information--which can be used to identify the amorphous state, follow its thermal and time relaxation, and establish the participation of conformational transformations of molecules in these processes--can be obtained by diffraction-spectral methods combining diffraction measurements with simultaneous recording of Raman lightscattering spectra. A detailed analysis is made of the possibility of investigating the density of vibrational states by inelastic neutron scattering and Raman scattering of light. The results obtained by electron spectroscopy are discussed in the specific case of the spectra of cold-deposited-films. Much attention is given to the method of selective laser spectroscopy. A hierarchy of universal properties of a molecular amorphous substance is proposed and it is shown that spectroscopy is the main method for investigating the majority of them.