One critical challenge for high-volume nanomanufacturing requires the on-line monitoring and measurement of the nanostructures manufactured. Computational metrology is expected to provide a novel means for fast, low-cost, nondestructive, and accurate measurement in high-volume manufacturing. Computational metrology refers to a measurement method where a complicated measurement process is modeled as a forward problem and some measured data are obtained by a specific instrument under a certain measurement configuration, and then the measurands are precisely and accurately reconstructed by solving the corresponding inverse problem. Thus computational metrology is essentially a model-based metrology and a typical process to solve an inverse problem. The key issues in computational metrology, such as the measurability, the measurement error analysis and precision estimation, the measurement configuration optimization, the fast and accurate forward modeling, and the fast and robust measurand reconstruction, and their generalized solution methods are explored in this paper, with an emphasis on the significance and necessity to apply modern mathematical theories and tools in solving the related problems. Some case studies carried out in my research group are presented to demonstrate the capability of computational metrology.