Process optimization in equation-oriented (EO) modeling environments favors the gradient-based opti-mization algorithms by their abilities to provide accurate Jacobian matrices via automatic or symbolic differentiation.However,computational inefficiencies including that in initial-point-finding for Newton type methods have significantly limited its application.Recently,progress has been made in using a pseudo-transient (PT) modeling method to address these difficulties,providing a fresh way for-ward in EO-based optimization.Nevertheless,research in this area remains open,and challenges need to be addressed.Therefore,understanding the state-of-the-art research on the PT method,its principle,and the strategies in composing effective methodologies using the PT modeling method is necessary for further developing EO-based methods for process optimization.For this purpose,the basic concepts for the PT modeling and the optimization framework based on the PT model are reviewed in this paper.Several typical applications,e.g.,complex distillation processes,cryogenic processes,and optimizations under uncertainty,are presented as well.Finally,we identify several main challenges and give prospects for the development of the PT based optimization methods.