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Mobile cloud computing (MCC) integrates cloud computing (CC) into mobile networks, prolonging the battery life of the mobile users (MUs). However, this mode may cause significant execution delay. To address the delay issue, a new mode known as mobile edge computing (MEC) has been proposed. MEC provides computing and storage service for the edge of network, which enables MUs to execute applications efficiently and meet the delay requirements. In this paper, we present a comprehensive survey of the MEC research from the perspective of service adoption and provision. We first describe the overview of MEC, including the definition, architecture, and service of MEC. After that we review the existing MUs-oriented service adoption of MEC, i.e., offloading. More specifically, the study on offloading is divided into two key taxonomies: computation offloading and data offloading. In addition, each of them is further divided into single MU offloading scheme and multi-MU offloading scheme. Then we survey edge server- (ES-) oriented service provision, including technical indicators, ES placement, and resource allocation. In addition, other issues like applications on MEC and open issues are investigated. Finally, we conclude the paper.