The food industry is striving for a sustainable development of thermal food processing. Smoking is an example of a process that has grown in popularity in recent years. There is a lack of systematic knowledge in the literature regarding this undervalued process, so the purpose of this review is to analyze the state of knowledge about the methods and technologies of smoking food products and their impact on changing the quality of essential food products. Therefore, a comprehensive review of the literature on smoking processes from the past two decades was conducted. The most essential components absorbed from smoke during smoking are polycyclic aromatic hydrocarbons (PAHs). In the present work, 24 PAHs are summarized, and the capability of 12 food products to absorb them is described. Analysis of the principal components of absorbed PAHs showed that some products from different groups exhibit a similar ability to absorb these compounds, mainly influenced by their physical properties. The pre-treatment practices of raw materials before smoking, the smoking raw materials used, and their quality parameters were characterized (along with the effects of smoking methods on selected product groups: fish, meats, and cheeses). In addition, the gap in research concerning the absorption of other components of smoke, e.g., phenols, alcohols, ketones, and aldehydes, which directly impact food quality, is indicated.