Moving-horizon estimation (MHE) is an optimization-based strategy for process monitoring and state estimation. One may view MHE as an extension for Kalman filtering for constrained and nonlinear processes. MHE therefore, subsumes both Kalman and extended Kalman filtering. In addition, MHE allows one to include constraints in the estimation problem. One can significantly improve the quality of state estimates for certain problems by incorporating prior knowledge in the form of inequality constraints. Inequality constraints provide a flexible tool for complementing process knowledge. One also may use inequality, constraints as a strategy for model simplification. The ability to include constraints and nonlinear dynamics is what distinguishes MHE from other estimation strategies. Both the practical and theoretical issues related to MHE are discussed. Using a series of example monitoring problems, the practical advantages of MHE are illustrated by demonstrating how the addition of constraints can improve and simplify the process monitoring problem.