Executable software architecture descriptions enable architects to validate or verify the correctness of their designs early in the development process of software-intensive systems, reducing the risk of costly misconceptions. Executable architectures have been the subject of research for several decades, but there is no comprehensive panorama of the state of the art on this topic. To fill this gap, we conducted a systematic mapping study that explores activities and approaches related to executable architecture descriptions for designing software-intensive systems. We have selected and analyzed 45 studies from the last 30 years to understand the activities related to executing architecture descriptions and identify the existing approaches. We also devised a taxonomy with key concepts related to executable architecture descriptions for software-intensive systems. The resulting insights from our study can help researchers pinpoint areas for further investigation.