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The advent of the Internet of Things brings a wave of research, technology, and computing. The Internet of Things has brought a concept called the fog computing, which has launched many discussions in the scientific community. In a fog environment, a requested service decomposed into a set of tasks and applied with an optimal approach to schedule these tasks across the fog devices to serve the user requirements is an important challenge. In spite of the task scheduling approaches being a necessity in fog computing, to the best of our knowledge, there is no comprehensive survey in the field of task scheduling approaches in fog computing. This paper provides a survey to analyze the current research studies in task scheduling approaches in fog computing from 2015 to 2018. Moreover, this paper classifies the task scheduling approaches in two fields: static and dynamic. This study tries to discuss the advantages and disadvantages of each study to solve their weaknesses. Providing a survey of the task scheduling approaches in the fog computing, planning a technical taxonomy for the task scheduling approaches, and highlighting the future open issues in the recent topics are the contributions of this study.