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Smartphones are pervasively used in society, and have been both the target and victim of malware writers. Motivated by the significant threat that presents to legitimate users, we survey the current smartphone malware status and their propagation models. The content of this paper is presented in two parts. In the first part, we review the short history of mobile malware evolution since 2004, and then list the classes of mobile malware and their infection vectors. At the end of the first part, we enumerate the possible damage caused by smartphone malware. In the second part, we focus on smartphone malware propagation modeling. In order to understand the propagation behavior of smartphone malware, we recall generic epidemic models as a foundation for further exploration. We then extensively survey the smartphone malware propagation models. At the end of this paper, we highlight issues of the current smartphone malware propagation models and discuss possible future trends based on our understanding of this topic.