Positron emission particle tracking (PEPT) is a new technique allowing the quantitative study of flow phenomena in three dimensions in opaque systems that cannot be studied by techniques based on optical methods such as particle image velocimetry (PIV) or Laser Doppler anemometry (LDA). Here, the technique is initially described along with studies validating the technique, comparing velocity profiles from a Rushton and a pitched blade turbine in turbulent transparent systems from PEPT with PIV and LDA. Subsequently, results are presented showing, for the first time, the spatial distribution of suspended particles of two sizes throughout the vessel; and velocity profiles for the solid and liquid phase in low viscosity and high solid concentration three-phase (s-g-l) systems under fully turbulent conditions. Finally, three-dimensional flow fields, occupancy maps and Poincare maps are presented, again for the first time, arising from the mixing of two different non-Newtonian shear thinning yield stress slurries. Clearly, PEPT offers many possibilities for obtaining quantitative data previously unobtainable for a wide range of important mixing problems relevant to a broad spectrum of the process industries.