During the past few decades, remote sensing has been established as an innovative, effective and cost-efficient option for the provision of high-quality information concerning infrastructure to governments or decision makers in order to update their plans and/or take actions towards the mitigation of the infrastructure risk. Meanwhile, climate change has emerged as a serious global challenge and hence there is an urgent need to develop reliable and cost-efficient infrastructure monitoring solutions. In this framework, the current study conducts a comprehensive review concerning the use of different remote-sensing sensors for the monitoring of multiple types of infrastructure including roads and railways, dams, bridges, archaeological sites and buildings. The aim of this contribution is to identify the best practices and processing methodologies for the comprehensive monitoring of critical national infrastructure falling under the research project named “PROION”. In light of this, the review summarizes the wide variety of approaches that have been utilized for the monitoring of infrastructure and are based on the collection of remote-sensing data, acquired using the global navigation satellite system (GNSS), synthetic aperture radar (SAR), light detection and ranging (LiDAR) and unmanned aerial vehicles (UAV) sensors. Moreover, great emphasis is given to the contribution of the state-of-the-art soft computing methods throughout infrastructure monitoring aiming to increase the automation of the procedure. The statistical analysis of the reviewing publications revealed that SARs and LiDARs are the prevalent remote-sensing sensors used in infrastructure monitoring concepts, while regarding the type of infrastructure, research is orientated onto transportation networks (road and railway) and bridges. Added to this, deep learning-, fuzzy logic- and expert-based approaches have gained ground in the field of infrastructure monitoring over the past few years.