There has been a surge of interest in artificial intelligence and machine learning (AI/ML)-based medical devices. However, it is poorly understood how and which AI/ML-based medical devices have been approved in the USA and Europe. We searched governmental and non-governmental databases to identify 222 devices approved in the USA and 240 devices in Europe. The number of approved AI/ML-based devices has increased substantially since 2015, with many being approved for use in radiology. However, few were qualified as high-risk devices. Of the 124 AI/ML-based devices commonly approved in the USA and Europe, 80 were first approved in Europe. One possible reason for approval in Europe before the USA might be the potentially relatively less rigorous evaluation of medical devices in Europe. The substantial number of approved devices highlight the need to ensure rigorous regulation of these devices. Currently, there is no specific regulatory pathway for AI/ML-based medical devices in the USA or Europe. We recommend more transparency on how devices are regulated and approved to enable and improve public trust, efficacy, safety, and quality of AI/ML-based medical devices. A comprehensive, publicly accessible database with device details for Conformité Européene (CE)-marked medical devices in Europe and US Food and Drug Administration approved devices is needed.