(1) Background: The purpose of this review is to analyze domestic and foreign studies on the role of collagen-encoding genes polymorphism in the development of intervertebral discs (IVDs) degeneration in humans. (2) Methods: We have carried out a search for full-text articles published in e-Library, PubMed, Oxford Press, Clinical Case, Springer, Elsevier and Google Scholar databases. The search was carried out using keywords and their combinations. The search depth was 5 years (2016–2021). In addition, this review includes articles of historical interest. Despite an extensive search, it is possible that we might have missed some studies published in recent years. (3) Results: According to the data of genome-wide and associative genetic studies, the following candidate genes that play a role in the biology of IVDs and the genetic basis of the processes of collagen degeneration of the annulus fibrosus and nucleus pulposus of IVDs in humans are of the greatest interest to researchers: COL1A1, COL2A1, COL9A2, COL9A3, COL11A1 and COL11A2. In addition, the role of genes COL1A2, COL9A1 and others is being actively studied. (4) Conclusions: In our review, we summarized and systematized the available information on the role of genetic factors in IVD collagen fibers turnover and also focused on the functions of different types of collagen present in the IVD. Understanding the etiology of impaired collagen formation can allow doctors to prescribe pathogenetically-based treatment, achieving the most effective results.