Microgels are microscopic gel particles that are swollen by a solvent.  Composed of porous, elastic networks of cross-linked polymers, microgels are soft colloids that can encapsulate dye molecules or drugs.  Their sensitive response to environmental conditions (e.g., temperature and pH) and influence on flow properties suit microgels to widespread applications in the chemical, pharmaceutical, food, and consumer care industries.  When dispersed in water, polyelectrolyte gels can become charged through dissociation of counterions.  Permeability and a tunable interplay between electrostatic and elastic forces give ionic microgels unique materials properties.  Within a coarse-grained model, we combine Poisson-Boltzmann theory of polyelectrolytes, Flory theory of network swelling, and molecular simulation to compute the osmotic pressure inside a single microgel particle and within bulk dispersions.  Predictions for particle swelling and bulk phase behavior can be tested against experiments, with potential relevance for chemical sensing and drug delivery.