The nonlinear theory of oscillating systems has introduced new aspects to the study of variable stars. Beyond the comparison of linear periods and the estimate of stability, the appearance and disappearance of possible models can be studied in detail. While nonlinearity in stellar pulsations is not a very complicated concept, it generally requires extensive and sometimes sophisticated numerical studies. The development of appropriate computational tools has allowed us to apply the nonlinear theory to real phenomena in variable stars. The International Astronomical Union Colloquium No. 134 presents a review of the new frontiers of variable star studies, one which will encourage further development of this field.