Structural health monitoring is an evaluation technology to monitor aerospace structure using sensing systems such as accelerometers, ultrasound wave response, images, and videos. In this field, there are three major steps: damage detection, localization, and quantification. The data accused from numerous detectors are commonly high dimensional and highly correlated. A critical challenge is manipulating noisy and lossy data to compress, transfer, and retrieve. Furthermore, to diagnose and prognosis of the existing damage, the relevant and valuable features should be extracted to have a physical meaning or reasonable interpretation. This research reviewed high dimensional data analysis methods like functional data analysis, tensor-based data analysis, compressive sensing, and matrix completion. The previous applications in structural health monitoring and nondestructive testing for aerospace structures are presented, and the potential researches can take advantage of high dimensional analysis methods are proposed.