Recently, several new tools and techniques have been developed which allow for robust detection and prediction of future planetary encounters and potential impacts by Near-Earth Asteroids (NEAs). We review the recent history of impact prediction theory, and cover the classical linear techniques for analyzing encounters, consisting of precise orbit determination and propagation followed by target plane analysis. When the linear approximation is unreliable there are various suitable approaches for detecting and analyzing very low probability encounters dominated by strongly nonlinear dynamics. We also describe an analytic approach that can provide valuable insight into the mechanisms responsible for most encounters. This theory is the foundation of the impact monitoring systems, the ones currently operational and the ones being developed.