This paper addresses the problem of estimating and controlling linear systems under adversarial attacks on sensors and actuators. The authors propose a novel estimation algorithm inspired by error-correction over the reals and compressed sensing, which is robust to attacks and computationally efficient. They also show that the design of resilient output feedback controllers can be reduced to the design of resilient state estimators. The paper first characterizes the resilience of a system to attacks and proposes an efficient algorithm to estimate the state despite the attacks. It then considers the problem of designing output-feedback controllers that stabilize the system despite attacks, showing that the separation between estimation and control holds. The authors demonstrate that the number of correctable errors is determined by the support of the system's observability matrix and that the maximum number of correctable errors is related to the number of sensors. They also show that by using state feedback, the number of correctable errors can be increased while maintaining control performance. The paper concludes with an optimization formulation of the optimal decoder and a relaxation of the optimal decoder using the $\ell_1$ norm.This paper addresses the problem of estimating and controlling linear systems under adversarial attacks on sensors and actuators. The authors propose a novel estimation algorithm inspired by error-correction over the reals and compressed sensing, which is robust to attacks and computationally efficient. They also show that the design of resilient output feedback controllers can be reduced to the design of resilient state estimators. The paper first characterizes the resilience of a system to attacks and proposes an efficient algorithm to estimate the state despite the attacks. It then considers the problem of designing output-feedback controllers that stabilize the system despite attacks, showing that the separation between estimation and control holds. The authors demonstrate that the number of correctable errors is determined by the support of the system's observability matrix and that the maximum number of correctable errors is related to the number of sensors. They also show that by using state feedback, the number of correctable errors can be increased while maintaining control performance. The paper concludes with an optimization formulation of the optimal decoder and a relaxation of the optimal decoder using the $\ell_1$ norm.