This paper discusses the state of advancement in the development of spectroscopic methods based on the use of mid (proper) infrared radiation in the context of applications in various fields of science and technology. The authors drew attention to the most important solutions specific to both spectroscopy itself (ATR technique) and chemometric data processing tools (PCA and PLS models). The objective of the current paper is to collect and consistently present information on various aspects of FT-IR spectroscopy, which is not only a well-known and well-established method but is also continuously developing. The innovative aspect of the current review is to show FT-IR’s great versatility that allows its applications to solve and explain issues from both the scientific domain (e.g., hydrogen bonds) and practical ones (e.g., technological processes, medicine, environmental protection, and food analysis). Particular attention was paid to the issue of hydrogen bonds as key non-covalent interactions, conditioning the existence of living matter and determining the number of physicochemical properties of various materials. Since the role of FT-IR spectroscopy in the field of hydrogen bond research has great significance, a historical outline of the most important qualitative and quantitative hydrogen bond theories is provided. In addition, research on selected unconventional spectral effects resulting from the substitution of protons with deuterons in hydrogen bridges is presented. The state-of-the-art and originality of the current review are that it presents a combination of uses of FT-IR spectroscopy to explain the way molecules vibrate and the effects of those vibrations on macroscopic properties, hence practical applications of given substances.