As long as industrial robots are programmed by teachprogramming, their positioning accuracy is unimportant.With a wider implementation of offline programmingand new applications such as machining, ensuringa higher positioning accuracy of industrial robotsover the entire working space has become very important.In this paper, we first review the measurementschemes of end effector poses. We then outline kinematicmodelsof serial articulated industrialmanipulatorsto quantify the positioning accuracy with a focuson the extension of the classical Denavit-Hartenberg(DH) models to include rotary axis error motions.Subsequently, we expand the discussion on kinematicmodels to compliant robot models. The review highlightscompliance models that are applied to calculatethe elastic deformation produced by forces, namelygravity and external loads. Model-based numericalcompensation plays an important role in machine toolcontrol. This paper aims to present state-of-the-arttechnical issues and future research directions for theimplementation of model-based numerical compensationschemes for industrial robots.