Abstract: Elastic mobile cloud computing (EMCC) enables the seamless and transparent use of cloud resource to augment the capability of mobile devices by off-loading parts of mobile devices’ tasks to cloud according to the real-time user requirement. By summarizing the service providing models of EMCC, we divide existing EMCC models into two categories: computing migration-mobile cloud computing(CM-MCC), in which the mobile devices employ the cloud to perform the parts of their computing intensive tasks; and cloud agent-mobile cloud computing(CA-MCC), in which the cloud maintains one or more virtual mobile devices for each mobile device and these virtual mobile devices are synchronized with the mobile device to complete various tasks such as computing, storage, security and communication instead of the mobile device. Then the applicable scenarios, the implementation method, the key issues, and the future research of EMCC models in each category are studied. After that, we analyze the critical security threats of EMCC, including users’ error operations or malicious actions, malicious applications, communications security problems, and cloud computing security issues such as the vulnerabilities of virtual system, multi-tenant problems, malicious cloud service providers. The corresponding defenses of these threats are discussed. At last, we point out that security is a key issue for EMCC.