An overview will be given of the mathematical models and solution methodologies that have been developed in recent years to interpret a variety of electrokinetic phenomena in hydrogels, particularly nanoparticle gel electrophoresis and electroacoustic spectroscopy. In nanoparticle electrophoresis, an electric field drives the steady translation of nanoparticles through the hydrogel pores. When particles have a weak physicochemical interaction with the skeleton, their electrophoretic mobility is dominated by the electrokinetic influences that arise from perturbations to Poisson-Boltzmann equilibrium. If the electric field oscillates at megahertz frequencies, then collective nanoparticle motion generates sound waves, the pressure spectrum (termed the electrokinetic-sonic-amplitude) of which can be related to nanoparticle and hydrogel properties, such as nanoparticle size and charge, and hydrogel permeability and viscoelasticity. In the steady and oscillatory regimes, the nanoparticle-doped hydrogel conductivity and dielectric spectra furnish additional diagnostics that can be used to compare theory and experiment. Aspects of these problems that have furnished compelling comparisons to experiments, and those that present ongoing challenges, will be highlighted.