Background: Chronic non-malignant pain represents a growing global public health priority. Chronic pain is multifactorial, with numerous biological, psychological, and social factors contributing to this pain syndrome. It affects not only the patients, impairing their quality of life, but also their family and social environment. Chronic pain is a diagnosis and requires effective and sustainable treatment strategies. Objective: Our aim was to critically review the available evidence on the importance of different approaches in treating patients with chronic non-malignant pain, emphasizing the effectiveness of integrating psychological and social factors within a multidisciplinary framework. Methods: This was a non-systematic narrative review of the basic and recent literature analyzing approaches to the treatment of chronic non-malignant pain. The inclusion criteria for the papers were chronic non-malignant pain, treatment approach, review, and original research papers published in English in the last five years (PubMed search), and the basic literature was selected from the references of new papers according to the knowledge and experience of the authors. Results: This literature review included 120 papers, of which 83 were basic, and 37 were new, published in the last 5 years (2018–2023). The results show that both the basic and newly published literature advocate for a biopsychosocial approach to treating chronic pain. Conclusions: New findings, compared to the earlier literature, indicate a new classification of chronic pain into primary and secondary. Chronic pain should be approached with a biopsychosocial model within a multidisciplinary treatment framework. This model addresses the complex interplay of biological, psychological, and social factors, offering a holistic strategy for effective pain management.