Braiding is an advanced textile manufacturing method that is used to produce two-dimensional and three-dimensional components. Unlike laminated structures, braids have interlaced yarns that form a continuity between layers. This structure allows for improved impact resistance, damage tolerance, and improved through-thickness reinforcement. Despite the numerous advantages of braided composites, braids also have shortcomings. Their highly complex fiber architecture presents challenges in the availability and choice of the strain measuring and characterization techniques. Advanced measurement methods such as optical strain measurement, micro-computed tomography, and in situ strain measurement are required. Optical strain measurement methods such as digital image correlation and high-speed imaging are necessary to accurately measure the complex deformation and failure that braided composites exhibit. X-ray-based micro-computed tomography measurements can provide detailed geometric and morphologic information for braided structures, which is necessary for accurately predicting the mechanical properties of braided structures. Finally, in situ strain measurement methods will provide detailed information on the internal deformation and strain that exists within braided structures. In situ sensors will also allow for in-service health monitoring of braided structures. This paper provides a detailed review of the aforementioned sensing technologies and their relation to the measurement of braided composite structures.