In contemporary scientific research, it is often of great interest to predict a categorical response based on a high-dimensional tensor and additional covariates. Motivated by applications in science and engineering, we propose a comprehensive and interpretable discriminant analysis model, called the CATCH model. The CATCH model efficiently integrates the covariates and the tensor to predict the categorical outcome. It also jointly explains the complicated relationships among the covariates, the tensor predictor, and the categorical response. The tensor structure is utilized to achieve easy interpretation and accurate prediction. To tackle the new computational and statistical challenges arising from the intimidating tensor dimensions, we propose a penalized approach to select a subset of the tensor predictor entries that affect classification after adjustment for the covariates. An efficient algorithm is developed to take advantage of the tensor structure in the penalized estimation. Theories and numerical studies demonstrate the favorable performance of CATCH. This talk is based on joint work with Yuqing Pan and Xin Zhang.