Masonry arch bridges constitute a significant proportion of European road and rail infrastructures.Most of them are well over 100 years old and are supporting traffic loads many times above those originally envisaged. The inherent variation in their constituent materials, the traditional design criteria and methods used for their construction, their deterioration over time caused by weathering processes and the development of other defects, significantly influence the mechanical response of these historic structures. A deep understanding on the numerous factors that affect the structural behaviour of masonry arch bridges and on the analysis methods to assess the life expectancy of such bridges and inform maintenance and strengthening strategies is essential. This paper provides a critical review of the experimental studies that have been carried out and of the assessment approaches that have been developed in the last three decades to these aims. The current knowledge is established and areas of possible future research work are identified, with the aim of providing students and researchers, asset managers and bridge owners, and practitioners with a guidance for research activities and maintenace strategies.