This thesis applies knowledge of the physical dynamics of objects to estimating object motion from vision when estimation from vision alone fails. It differentiates itself from existing physics-based vision by building in robustness to situations where existing visual estimation tends to fail: fast motion, blur, glare, distractors, and partial or full occlusion. A real-time physics simulator is incorporated into a stochastic framework by adding several different models of how noise is injected into the dynamics. Several different algorithms are proposed and experimentally validated on two problems: motion estimation and object tracking. The performance of visual motion estimation from colour histograms of a ball moving in two dimensions is improved considerably when a physics simulator is integrated into a MAP procedure involving non-linear optimisation and RANSAC-like methods. Process noise or initial condition noise in conjunction with a physics-based dynamics results in improved robustness on hard visual problems. A particle filter applied to the task of full 6D visual tracking of the pose an object being pushed by a robot in a table-top environment is improved on difficult visual problems by incorporating a simulator as a dynamics model and injecting noise as forces into the simulator.