The variety of functionalities and porous structures inherent to metal-organic frameworks (MOFs) together with the facile tunability of their properties makes these materials suitable for a wide range of existing and emerging applications. Many of these applications are based on processes involving interaction of MOFs with guest molecules. To optimize a certain process or successfully design a new one, a thorough knowledge is required about the physicochemical characteristics of materials and the mechanisms of their interaction with guest molecules. To obtain such important information, various complementary analytical techniques are applied, among which vibrational spectroscopy (IR and Raman) plays an important role and is indispensable in many cases. In this review, we critically examine the reported applications of IR and Raman spectroscopies as powerful tools for initial characterization of MOF materials and for studying processes of their interaction with various gases. Both the advantages and the limitations of the technique are considered, and the cases where IR or Raman spectroscopy is preferable are highlighted. Peculiarities of MOFs interaction with specific gases and some inconsistent band assignments are also emphasized. Summarizing the broad analytical possibilities of the IR and Raman spectroscopies, we conclude that it can be applied in combinations with other techniques to explicitly establish the structure, properties, and reactivity of MOFs.