Nowadays, mobile applications are demanding compute-intensive use, in addition to the need for lower latency and lower computational costs. Thus, researchers are proposing to bring the computation of these applications closer to the users by offloading these applications to the Edge. In this work, we carried out a comprehensive literature review with the primary objective of investigating the offloading strategies used in the Edge Computing scenario, which restrictions are considered, and the security aspects considered by the strategies. From the selected works, we describe the main optimization objectives of the strategies, which models and algorithms were implemented, which computational constraints were considered, which types of applications, and the security requirements. Finally, we discussed some opportunities and open challenges.