Modern smartphones are equipped with various sensors along with on-board storage, computing and communication capabilities. Owing to these features, they can become an intelligent, scalable, autonomous and potentially cost-free component of the next generation civil infrastructure monitoring systems in future smart cities. Over the past few years, there has been a growing interest in the deployment of smartphone-based monitoring technologies within the civil engineering arena. Overall, the smartphone sensing paradigm is still in its infancy, with great promise for researchers to rapidly expand its many potential applications. This paper presents a comprehensive literature review of smartphone-centric research for the monitoring of civil infrastructure systems. The historical deployment of smartphones in major areas of civil engineering has been explored. An emphasis is placed on sensing capabilities of smartphones and their crowdsourcing power for monitoring several distinct civil infrastructure systems. Furthermore, a case study is presented to provide our most recent efforts in deployment of smartphones for evaluation of highway pavements and challenges ahead. Finally, limitations, challenges and future directions for widespread application of smartphone-driven monitoring systems are discussed. The survey implies that much research is still required to explore the power of crowdsourced smartphone-based measurements, and to branch out into new application domains.