Many models and methodologies are available to deal with imperfect repair for repairable systems. Initial attempts at modeling imperfect repair using the (p, q) rule that defined the two extremities of imperfect repair-perfect renewal and minimal repair were effectively extended by Kijima and Sumita. They developed the generalized renewal theory from the renewal theory in the context of imperfect repair and applied it to repairable systems with the concept of virtual age. Since this pioneering work, much of imperfect repair modeling literature builds up on Kijima's models based on the Generalized Renewal Process (GRP). The paper conducts a survey for imperfect repair of repairable systems using GRP based on arithmetic reduction of age (ARA) and arithmetic reduction of intensity (ARI) concepts in general and Kijima models in particular. In addition to the theoretical development of Kijima models and its extensions, the review highlights their applications such as designing maintenance policies based on the concept of ARA. The survey will be useful to researchers in providing a starting point to develop appropriate models that suit their application oriented requirements. © 2013 Elsevier Ltd.