A descriptor system approach is introduced to investigate sensor fault reconstruction and sensor compensation for a class of nonlinear state-space systems with Lipschitz constraints. Letting the sensor fault term be an auxiliary state vector, an augmented descriptor system is constructed. Using the linear matrix inequality technique, a state-space nonlinear estimator is designed for the augmented descriptor plant. Accurate asymptotic estimates of the original system state vector and the sensor fault term are thus obtained readily. By subtracting the estimated sensor fault term from the measurement output, sensor compensation is performed, allowing the existing controller for the original plant (without sensor faults) to continue to function normally even when a sensor fault occurs. Robust sensor fault reconstruction and sensor compensation are also discussed in detail for systems with simultaneous sensor faults, input disturbances and output noises. Finally, numerical examples and simulations are given to illustrate the design procedures and demonstrate the efficiency of the approaches. The sensor fault considered may be in any form, and may even be unbounded. As a result, the present work possesses a wide scope of applicability.