While there is a clear clinical benefit of oral anticoagulation in patients with atrial fibrillation (AF) and venous thromboembolism (VTE) in reducing the risks of thromboembolism, major bleeding events (especially intracranial bleeds) may still occur and be devastating. The decision for initiating and continuing anticoagulation is often based on a careful assessment of both thromboembolism and bleeding risk. The more common and validated bleeding risk factors have been used to formulate bleeding risk stratification scores, but thromboembolism and bleeding risk factors often overlap. Also, many factors that increase bleeding risk are transient and modifiable, such as variable international normalized ratio values, surgical procedures, vascular procedures, or drug-drug and food-drug interactions. Bleeding risk is also not a static "one-off" assessment based on baseline factors but is dynamic, being influenced by aging, incident comorbidities, and drug therapies. In this executive summary of a European and Asia-Pacific Expert Consensus Paper, we comprehensively review the published evidence and propose a consensus on bleeding risk assessments in patients with AF and VTE, with a view to summarizing "best practice" when approaching antithrombotic therapy in these patients. We address the epidemiology and size of the problem of bleeding risk in AF and VTE, and review established bleeding risk factors and summarize definitions of bleeding. Patient values and preferences, balancing the risk of bleeding against thromboembolism, are reviewed, and the prognostic implications of bleeding are discussed. We propose consensus statements that may help to define evidence gaps and assist in everyday clinical practice.