A system for manipulating and supporting a beating heart during cardiac surgery, including a gross support element for engaging and supporting the heart (the gross support element preferably including a head which is sized and shaped to cradle the myocardium of the left ventricle"), a suspension head configured to exert lifting force on the heart when positioned near the apical region of the heart at a position at least partially overlying the right ventricle, and a releasable attachment element for releasably attaching at least one of the gross support element and the suspension head to the heart. The releasable attachment element can be a mechanical element (such as one or more staples or sutures') or an adhesive such as glue. Alternatively, the system includes a suspension head and a releasable attachment element for releasably attaching it to the heart, but does not include a gross support element.