This research project is at the intersection of the fields of physics of nonlinear phenomena, applied mathematics, nonlinear analysis, and computation. Knowledge of liquid-crystal-based suspensions is currently advancing quite rapidly, motivated by applications in materials science as well as in biological systems. The research aims to develop a predictive theory of transport in suspensions within an anisotropic liquid crystalline matrix, including electrostatically charged particles and ions. The particles can have arbitrary shapes, be rigid or soft, charged or electrically neutral, or be domains of the isotropic-nematic phase transition (chromonics). Analysis and computation will be used to explore both static and time dependent problems. Primarily variational methods will be employed, either within energy minimization for static problems or within the minimum dissipation principle for time dependent problems. Novel theoretical aspects include comprehensive models of colloidal systems in structured media that incorporate elasticity of the nematic matrix, surface anchoring, electric field, ions, and flow and their interplay. Improved understanding of liquid crystal anchoring and defect dynamics will allow for higher resolution, faster display devices.