Tomato (Solanum lycopersicum L.) is one of the most commercially essential vegetable crops cultivated worldwide. In addition to the nutritional value, tomato is an excellent model for studying climacteric fruits’ ripening processes. Despite this, the available natural pool of genes that allows expanding phenotypic diversity is limited, and the difficulties of crossing using classical selection methods when stacking traits increase proportionally with each additional feature. Modern methods of the genetic engineering of tomatoes have extensive potential applications, such as enhancing the expression of existing gene(s), integrating artificial and heterologous gene(s), pointing changes in target gene sequences while keeping allelic combinations characteristic of successful commercial varieties, and many others. However, it is necessary to understand the fundamental principles of the gene molecular regulation involved in tomato fruit ripening for its successful use in creating new varieties. Although the candidate genes mediate ripening have been identified, a complete picture of their relationship has yet to be formed. This review summarizes the latest (2017–2023) achievements related to studying the ripening processes of tomato fruits. This work attempts to systematize the results of various research articles and display the interaction pattern of genes regulating the process of tomato fruit ripening.