Tomographic measurement techniques offer new opportunities and challenges for quantifying the degree of mixing of particulate suspensions and other multiphase mixtures. This has implications for the design, operation and control of industrial mixers and batch reactors, including crystallizers. Various statistical methods for describing mixing phenomena are reviewed and selected methods are applied to electrical resistance and positron emission data. New and more robust methods of image reconstruction and interpretation are reported for electrical tomography based on discretizing the mixer volume into a small number of regions or cells. Realistic models can be proposed and reconstruction can then be performed by modification of existing (Newton-Raphson) methods or, if these become too complex, by the application of the Metropolis algorithm or Markov chain Monte Carlo methods. Reducing the number of parameters of the associated model can remove ambiguity and allow rapid reconstruction. Improvements to instrumentation hardware and the mounting of electrical resistance sensors on the impeller shaft greatly assists the analysis of regions of interest (such as the vicinity of down-comers). The resulting linked design and analysis of the entire measurement system with a Bayesian parametric-reconstruction approach is a significant advance in tomographic technology.