Non-pneumatic tyre technology can overcome the safety problems of traditional pneumatic tyres. Hence, it is expected to improve driving safety significantly. Accordingly, in recent years, this technology has received extensive attention. This paper reviews the status of research of non-pneumatic tyres and discusses their development trends. Initially, the fundamental concept of non-pneumatic tyres is introduced, and their structural characteristics are described in detail. Subsequently, the research progress on the material properties of non-pneumatic tyre components is summarised. The research results on the mechanical properties of non-pneumatic tyres are recapitulated in terms of vertical mechanical, longitudinal mechanical, lateral mechanical, grounding, vibration, and fatigue characteristics. Moreover, the advantages and disadvantages of non-pneumatic tyres are analysed. Three prevailing forming technologies and tyre performance tests are discussed. The application of intelligent materials and structures to non-pneumatic tyres is proposed for these tyres to be lightweight, functional, and intelligent. Finally, the technical problems that must be resolved in the study of non-pneumatic tyres and the anticipated development trends are presented in this paper.