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Proliferation of Industrial Internet has dramatically changed the way we live and work. It brings convenience to our society and sometimes requires real-time processing of dramatic data at the same time. However, traditional paradigm of computing on the center cloud can't always meet such requirement, for the non-negligible time delay of data transmission and communication. Edge computing is a novel computing paradigm proposed to resolve such a problem. As a promising technology, it extends computing from cloud center to the edge of network. Edge computing has the advantage of low latency to achieve a shorter response time, as well as potential to address the concerns of energy consuming, bandwidth burden and security issue. In this paper, we give a survey about edge computing from the aspect of methodologies, application scenarios and its role in Industrial Internet. Some open issues of edge computing are also introduced in this paper. At the end of the manuscript, a discussion about future direction is proposed. The shallow network algorithms such as broad learning system (BLS), which have achieved great improvement in computing efficiency, show an optimistic outlook in this area. We propose our conceive about future applications when shallow network methods like BLS are applied in edge computing and hope the paper will inspire research in relative directions. [ABSTRACT FROM AUTHOR]