Built cultural heritage is under constant threat due to environmental pressures, anthropogenic damages, and interventions. Understanding the preservation state of monuments and historical structures, and the factors that alter their architectural and structural characteristics through time, is crucial for ensuring their protection. Therefore, inspection and monitoring techniques are essential for heritage preservation, as they enable knowledge about the altering factors that put built cultural heritage at risk, by recording their immediate effects on monuments and historic structures. Nondestructive evaluations with close-range sensing techniques play a crucial role in monitoring. However, data recorded by different sensors are frequently processed separately, which hinders integrated use, visualization, and interpretation. This article’s aim is twofold: i) to present an overview of close-range sensing techniques frequently applied to evaluate built heritage conditions, and ii) to review the progress made regarding the fusion of multi-sensor data recorded by them. Particular emphasis is given to the integration of data from metric surveying and from recording techniques that are traditionally non-metric. The article attempts to shed light on the problems of the individual and integrated use of image-based modeling, laser scanning, thermography, multispectral imaging, ground penetrating radar, and ultrasonic testing, giving heritage practitioners a point of reference for the successful implementation of multidisciplinary approaches for built cultural heritage scientific investigations.