CCTV cameras installed for continuous surveillance generate enormous amounts of data daily, forging the term Big Video Data (BVD). The active practice of BVD includes intelligent surveillance and activity recognition, among other challenging tasks. To efficiently address these tasks, the computer vision research community has provided monitoring systems, activity recognition methods, and many other computationally complex solutions for the purposeful usage of BVD. Unfortunately, the limited capabilities of these methods, higher computational complexity, and stringent installation requirements hinder their practical implementation in real-world scenarios, which still demand human operators sitting in front of cameras to monitor activities or make actionable decisions based on BVD. The usage of human-like logic, known as fuzzy logic, has been employed emerging for various data science applications such as control systems, image processing, decision making, routing, and advanced safety-critical systems. This is due to its ability to handle various sources of real-world domain and data uncertainties, generating easily adaptable and explainable data-based models. Fuzzy logic can be effectively used for surveillance as a complementary for huge-sized artificial intelligence models and tiresome training procedures. In this article, we draw researchers’ attention toward the usage of fuzzy logic for surveillance in the context of BVD. We carry out a comprehensive literature survey of methods for vision sensory data analytics that resort to fuzzy logic concepts. Our overview highlights the advantages, downsides, and challenges in existing video analysis methods based on fuzzy logic for surveillance applications. We enumerate and discuss the datasets used by these methods, and finally provide an outlook toward future research directions derived from our critical assessment of the efforts invested so far in this exciting field.