By adjusting their chemical composition and selecting appropriate polymers and synthesis pathways, the swelling properties and effective electrostatic interactions of polyelectrolyte microgels can be tuned for specific applications. However, the extensive variety of materials available for synthesizing and functionalizing them, along with the complex coupling between material properties, microgel architecture and emergent properties such as the equilibrium swelling and net charge, makes microgel synthesis exploration an arduous and expensive endeavor. Fine-tuning microscopic features of the microgels for specific materials to attain the desired suspension behavior is equally demanding. Hence, the availability of analytical and semi-analytical theoretical models that provide guidance during experimental exploration or serve as references for more costly simulations, is immensely valuable. Furthermore, theoretical models help in the interpretation of experimental data as well as in the fundamental understanding of the swelling behavior.