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In recent times, Wireless Sensor Networks (WSNs) are broadly applied in the Industrial Internet of Things (IIoT) in order to enhance the productivity and efficiency of existing and prospective manufacturing industries. In particular, an area of interest that concerns the use of WSNs in IIoT is the concept of sensor network virtualization and overlay networks. Both network virtualization and overlay networks are considered contemporary because they provide the capacity to create services and applications at the edge of existing virtual networks without changing the underlying infrastructure. This capability makes both network virtualization and overlay network services highly beneficial, particularly for the dynamic needs of IIoT based applications such as in smart industry applications, smart city, and smart home applications. Consequently, the study of both WSN virtualization and overlay networks has become highly patronized in the literature, leading to the growth and maturity of the research area. In line with this growth, this paper provides a review of the development made thus far concerning virtualized sensor networks, with emphasis on the application of overlay networks in IIoT. Principally, the process of virtualization in WSN is discussed along with its importance in IIoT applications. Different challenges in WSN are also presented along with possible solutions given by the use of virtualized WSNs. Further details are also presented concerning the use of overlay networks as the next step to supporting virtualization in shared sensor networks. Our discussion closes with an exposition of the existing challenges in the use of virtualized WSN for IIoT applications. In general, because overlay networks will be contributory to the future development and advancement of smart industrial and smart city applications, this review may be considered by researchers as a reference point for those particularly interested in the study of this growing field.