With the commercialization of advanced modulation and coding techniques, the system capacity is gradually approaching the Shannon limit. Nevertheless, traditional communication based on the Shannon information theory is confronted with bottlenecks. Semantic communication (SemCom) is a highly promising paradigm for breaking bottlenecks. However, existing SemCom lacks flexibility, interpretability, and robustness. To overcome these deficiencies, cognitive SemComs exploit external knowledge to realize brain-like reasoning during semantic transmission, which improves spectrum efficiency and communication reliability. This article aims to survey the latest research results in this direction. Important implementation issues of cognitive SemCom are examined. Moreover, a software-defined radio testbed is built to demonstrate the feasibility of the cognitive SemCom prototype. Finally, to guide future research directions, key challenges and open issues are discussed.