Industry 4.0 promotes manufacturing and process industry towards digitalization and intellectualization. Edge computing can provide delay-sensitive services in industrial processes to realize intelligent production. Lightweight virtualization technology is one of the key elements of edge computing, which can implement resource management, orchestration, and isolation services without considering heterogenous hardware. It has revolutionized software development and deployment. The scope of this review paper is to present an in-depth analysis of two such technologies, Container and Unikernel, for edge computing. We discuss and compare their applicability in terms of migration, security, and orchestration for edge computing and industrial applications. We describe their performance indexes, evaluation methods and related findings. We then discuss their applications in industrial processes. To promote further research, we present some open issues and challenges to serve as a road map for both researchers and practitioners in the areas of Industry 4.0, industrial process automation, and advanced computing.