Semantic web models such as ontologies and knowledge graphs were designed to represent knowledge explicitly and to infer implicit knowledge. This brings several benefits like flexibility and reasoning power. On the other hand, since the adoption of these models has been growing during the last years, the demand for consistency has risen in parallel. Therefore, the validation of these representations started to be an important issue for research. Several types of related works have been done; however, there is still a lack of an integrated review to understand the state of the art of formal semantic constraint validation. Addressing this issue is crucial for broader adoption of both the models discussed and the Semantic Web itself. For the community, it is important to review existing progress, outline future avenues, and examine related areas that can benefit from these developments. The contribution of this article includes a taxonomy of related research trends, a classification of selected works into these categories, and an overview of the main open challenges in validating semantic constraints for the Semantic Web. Each of these contributions was obtained through the conduction of a systematic literature review. In addition, an extension of the study is done to consider a very promising model which has a growing intersection with the field: property graphs. Finally, this paper concludes with an outlook that summarizes the contributions made and the challenges that the authors decided to continue researching in further steps.