By the late 1970s, plastics had emerged as the most widely used materials globally. The discovery, development, and processing of diverse polymeric materials have profoundly shaped modern life and driven the expansion of numerous industries. Given the widespread interest in the utilization of these materials, it has become increasingly imperative to design their life cycles from the outset. This approach aims to maximize their utility while minimizing their environmental footprint. This review aims to identify and analyze the key challenges in polymer processing applicable to both additive and formative manufacturing methods, emphasizing the relationship between processing and recycling within the framework of sustainability. Modern polymer processing techniques play a crucial role in enhancing the sustainability of polymer products by improving recycling potential (with consideration of polymer type, source, and additives), cost-effectiveness, carbon footprint, and key properties such as durability, lifespan, performance, and environmental impact. It will also explore the concept of the circular economy and its integration into modern processing methods, including extrusion, injection molding, and 3D printing. Additionally, current polymer recycling methods are analyzed with respect to their effectiveness, sustainability, and compatibility with the original materials. Moreover, the discussion emphasizes the benefits of a circular economy compared to a linear one by exploring the concepts of closed-loop and open-loop systems, along with their diverse applications depending on the material and the initial processing method employed. To ensure that humanity continues to benefit from polymer materials while striving for a waste-free environment, it is essential to integrate the principles of sustainable development from the very beginning.