The interest in airless or non-pneumatic tire (NPT) structures emerges due to potential performance and environmental advantages, such as reduced rolling resistance and improved recyclability, when compared with traditional rubber-based pneumatic tires. NPTs can already be found in commercial applications such as forklifts, electric scooters, and wheelchairs. Even so, up to the knowledge of authors, there is no known established large-scale production of NPTs for most applications. This work presents a systematic literature review regarding the mechanical design and development of NPTs. A summary of structural characteristics and mechanical behaviour analysis is provided. Relevant standards, analysis strategies, materials, production techniques, and the end-of-life of tires are addressed. In the end, the authors debate the current challenges and prospects of these emergent products. Furthermore, this research aims at being used as a tool, potentiating the development of innovative and efficient, airless tire solutions. The review presented clarifies that many academic efforts are focused on finding optimal functional designs, which are frequently complex and physically demanding. These geometrically complex design proposals are, in most cases, composed of intricate cellular structures and spokes arrangements. Based on the current lack of knowledge, authors identify key research areas to be further developed such as the production, performance, and reliability of NPTs. It is debatable whether there will ever be a shortcoming of the rubber tire, or a time when fully recyclable tires are a societal obligation. Nevertheless, the number of reasons to promote the development of a reliable replacement to the traditional tire is far from scarce.