By definition, biosimilar medicinal products are biological medicinal products that are similar to other biological medicinal products that are already on the market—the reference medicinal products. Access to biosimilar medicines is a current reality. However, to achieve this goal, it is extremely important to consistently and scientifically substantiate the regulatory requirements necessary for biosimilar medicines when accessing the market. Based on an analysis of the raw materials and the type of methods used in the manufacturing processes of biological medicines, it is known that this tends to be more complex for the quality of the finished product than the manufacture of molecules obtained through a chemical process. It is then relevant to highlight the main differences between both products: biological medicines manufactured using biotechnology and the current generics containing active pharmaceutical ingredients (APIs) obtained from synthetic processes. Once arriving at the approval process of these medicinal products, it is imperative to analyse the guidance documents and the regulatory framework that create the rules that allow these biosimilar medicinal products to come to the market. The present review aimed at documenting comparatively the specific provisions of European legislation, through the European Medicines Agency (EMA), as well as the legislation of the United States of America, through the Food and Drug Administration (FDA). This was then translated into a critical appraisal of what concerns the specific criteria that determine the favourable evaluation of a biosimilar when an application for marketing authorisation is submitted to different regulatory agencies. The gathered evidence suggests that the key to the success of biosimilar medicines lies in a more rigorous and universal regulation as well as a greater knowledge, acceptance, and awareness of health professionals to enable more patients to be treated with biological strategies at an earlier stage of the disease and with more affordable medicines, ensuring always the safety and efficacy of those medicines.