The irreversible marriage between digital technology and physical urban infrastructure has given rise to the concept of smart infrastructure. The potential benefits of smart infrastructure are significant; however, their realisation will depend on society's ability to address pressing issues, such as the need to develop a common language to describe terms and processes. This paper aims to lay out the foundations of such a common language. First, the authors review academic literature in order to outline key characteristics of so-called smart infrastructure systems. Importantly, the authors define and differentiate between smart and intelligent infrastructure systems. Then, the authors use an LVP framework to describe the levels (L), values (V) and principles (P) of inherently smart infrastructure systems. Finally, the authors argue that the study of smart infrastructure is a multidisciplinary field of research that reaches beyond traditional engineering and information technology disciplines. The authors expect that eliminating ambiguity and fragmentation in the definition of smart infrastructure systems will enhance research on and practice of these systems.