Mixing is intrinsically a Lagrangian process and, while Eulerian data are very important, Lagrangian information is necessary for its complete description. Lagrangian data can, in principle, be generated by using numerical simulations or experimental techniques based on Lagrangian tracking to provide the trajectories of fluid elements or particles. We present a set of theoretical and computational tools specifically developed for the analysis and validation of single-phase and multiphase Lagrangian flow data obtained from tracer trajectories in mechanically agitated vessels. The implementation and power of these tools are demonstrated by analyzing a wide range of measurements acquired using the technique of positron emission particle tracking during mixing of Newtonian and non-Newtonian fluids as well as mixing of concentrated solid-liquid suspensions. Finally, the accuracy of the raw Lagrangian data treatment developed here is illustrated by comparing with an Eulerian technique and showing very precise mass continuity for an agitated solid-liquid system. (C) 2011 American Institute of Chemical Engineers AIChE J, 58: 31-45, 2012