With the rapid developments in emerging mobile technologies, utilizing resource-hungry mobile applications such as media processing, online Gaming, Augmented Reality (AR), and Virtual Reality (VR) play an essential role in both businesses and entertainments. To soften the burden of such complexities incurred by fast developments of such serving technologies, distributed Mobile Edge Computing (MEC) has been developed, aimed at bringing the computation environments near the end-users, usually in one hop, to reach predefined requirements. In the literature, offloading approaches are developed to connect the computation environments to mobile devices by transferring resource-hungry tasks to the near servers. Because of some rising problems such as inherent software and hardware heterogeneity, restrictions, dynamism, and stochastic behavior of the ecosystem, the computation offloading issues consider as the essential challenging problems in the MEC environment. However, to the best of the author's knowledge, in spite of its significance, in machine learning-based (ML-based) computation offloading mechanisms, there is not any systematic, comprehensive, and detailed survey in the MEC environment. In this paper, we provide a review on the ML-based computation offloading mechanisms in the MEC environment in the form of a classical taxonomy to identify the contemporary mechanisms on this crucial topic and to offer open issues as well. The proposed taxonomy is classified into three main fields: Reinforcement learning-based mechanisms, supervised learning-based mechanisms, and unsupervised learning-based mechanisms. Next, these classes are compared with each other based on the essential features such as performance metrics, case studies, utilized techniques, and evaluation tools, and their advantages and weaknesses are discussed, as well. Finally, open issues and uncovered or inadequately covered future research challenges are argued, and the survey is concluded.