This paper presents a survey on Mobile Edge Computing (MEC), focusing on its architecture and computation offloading. MEC brings computation and storage resources to the edge of mobile networks, enabling high-demand applications to run at the User Equipment (UE) while meeting strict delay requirements. Unlike traditional cloud computing, MEC reduces latency and jitter by placing resources closer to UEs. It also allows operators and third parties to utilize these resources for specific purposes. The paper first describes major use cases and reference scenarios for MEC. It then surveys existing concepts integrating MEC into mobile networks and discusses current standardization efforts. The core of the survey is focused on computation offloading, which is divided into three key areas: decision on computation offloading, allocation of computing resources within MEC, and mobility management. The paper highlights lessons learned in MEC and discusses open research challenges. It also outlines several open challenges that need to be addressed to fully exploit MEC's potential. The paper concludes with a summary of general outcomes and draws conclusions. The paper also discusses various MEC concepts, including small cell cloud (SCC), mobile micro clouds (MMC), fast moving personal cloud (MobiScud), follow me cloud (FMC), and CONCERT. It also describes the ETSI MEC reference architecture and deployment options. The paper also introduces computation offloading as a critical use case for MEC, discussing factors influencing offloading decisions, such as execution delay, energy consumption, and application models. It also discusses the decision on computation offloading to MEC, focusing on minimizing execution delay, minimizing energy consumption while satisfying execution delay constraints, and finding a proper trade-off between both. The paper also discusses efficient allocation of computing resources within MEC and mobility management for moving users. The paper concludes with a summary of the key findings and challenges in MEC research.This paper presents a survey on Mobile Edge Computing (MEC), focusing on its architecture and computation offloading. MEC brings computation and storage resources to the edge of mobile networks, enabling high-demand applications to run at the User Equipment (UE) while meeting strict delay requirements. Unlike traditional cloud computing, MEC reduces latency and jitter by placing resources closer to UEs. It also allows operators and third parties to utilize these resources for specific purposes. The paper first describes major use cases and reference scenarios for MEC. It then surveys existing concepts integrating MEC into mobile networks and discusses current standardization efforts. The core of the survey is focused on computation offloading, which is divided into three key areas: decision on computation offloading, allocation of computing resources within MEC, and mobility management. The paper highlights lessons learned in MEC and discusses open research challenges. It also outlines several open challenges that need to be addressed to fully exploit MEC's potential. The paper concludes with a summary of general outcomes and draws conclusions. The paper also discusses various MEC concepts, including small cell cloud (SCC), mobile micro clouds (MMC), fast moving personal cloud (MobiScud), follow me cloud (FMC), and CONCERT. It also describes the ETSI MEC reference architecture and deployment options. The paper also introduces computation offloading as a critical use case for MEC, discussing factors influencing offloading decisions, such as execution delay, energy consumption, and application models. It also discusses the decision on computation offloading to MEC, focusing on minimizing execution delay, minimizing energy consumption while satisfying execution delay constraints, and finding a proper trade-off between both. The paper also discusses efficient allocation of computing resources within MEC and mobility management for moving users. The paper concludes with a summary of the key findings and challenges in MEC research.