The most comprehensive approach to understanding phase transitions and in particular critical phenomena is via the renormalization group (RG) theory. It has culminated in computational and perturbative analytic methods that have identified several universality classes and it has provided quantitative data categorizing the values of physical observables at those transitions. However, the predictive power, and thus the resulting quantitative data, for phase transitions in strongly coupled physics has been notoriously difficult to collect. After discussing the background of RG I will explain some recent work toward calculating the results of RG using analytic nonperturbative methods aimed at strongly coupled systems in general. In particular I will discuss a rescaling method applied to a complete basis of nonlinear states as well as a nonperturbative yet diagrammatic momentum shell RG method.