Autonomous monitoring of infrastructure systems offers a promising alternative to manual inspection techniques which are mostly tedious, expensive and prone to error. Robot-based autonomous monitoring systems not only provide higher precision, but they also allow frequent inspection of infrastructure systems at a much lower cost. Recent advancements in robotic systems have led to the development of reconfigurable swarm robots (RSR) that can change their shape and functionality dynamically, without any external intervention. RSR have the advantages of being modular, on-site reconfigurable, multifunctional, incrementally assemble-able, reusable, fault-tolerant, and even repairable on the orbit. Newly-developed reconfigurable robots are expected to bring a radical change in the prevailing structural health monitoring techniques, thus augmenting the efficiency, accuracy and affordability of inspection operations. This paper presents a holistic review of the previous studies and state-of-the-art technologies in the field of RSR, and argues that RSR offer great potential advantages from the perspective of monitoring and assessment of civil and mechanical systems. A roadmap for future research has also been outlined based on the limitations of the current methods and anticipated needs of future inspection systems.