Since the earliest works on the understanding of different forms of pulmonary hypertension, thrombosis has been involved in the pathophysiology of the disease, both in pulmonary arterial hypertension (PAH) and in chronic thromboembolic pulmonary hypertension (CTEPH). Autopsy and then pathophysiological data paved the way for the use of anticoagulants as a treatment for PAH and CTEPH. In PAH their role has diminished with the advent of specific targeted therapies, but they are still prescribed in more than half of PAH patients, because of concomitant venous thromboembolism or atrial fibrillation. In CTEPH long-term anticoagulant therapy is the cornerstone of the management. The recent development of direct oral anticoagulants (DOACs) raises the question of the best anticoagulation strategy, both in patients with PAH and in patients with CTEPH. In this review, we present an overview of the history of anticoagulants in the management of patients suffering from PAH or CTEPH, an update of the available data on the underlying rationale of their use in these subjects, an alert on the potential risks of using DOACs in these poorly explored situations, and the setting up of dedicated trials to evaluate the best anticoagulant treatment strategies in patients suffering from PAH or CTEPH.