Natural anticoagulant drugs can be obtained from plants, rich in secondary bioactive metabolites which, in addition to being effective antioxidants, also possess anticoagulant and antiplatelet properties and, for this reason, can be excellent candidates for the treatment of thrombotic diseases. This review reports an overview of the hemostatic process and thrombotic disorders together with data on plants, more and less common from around the world, containing bioactive compounds characterized by antiplatelet and anticoagulant activity. The reported literature was obtained from Medline, PubMed, Elsevier, Web of Science, Google Scholar considering only articles in the English language, published in peer-reviewed journals. The number of citations of the articles and the impact factor of the journals were other parameters used to select the scientific papers to be included in the review. The analysis of the literature data selected demonstrates that many plants’ bioactive compounds show antiplatelet and anticoagulant activity that make them potential candidates to be used as new natural compounds able to interfere with both primary and secondary hemostasis. Moreover, they could be used together with anticoagulants currently administered in clinical practice to increase their efficacy and to reduce complications in the treatment of thrombotic disorders.