The inaugural Kjell Johansen lecture in the Zoophysiology Department of Aarhus University (Aarhus, Denmark), afforded the opportunity for a focused workshop comprising comparative cardiovascular physiologists to ponder some of the key unanswered questions in the field. Discussions were centered around three themes. The first considered function of the vertebrate heart in its various forms in extant vertebrates, with particular focus on the role of intracardiac shunts, the trabecular (“spongy”) nature of the ventricle in many vertebrates, coronary blood supply and the building plan of the heart as revealed by molecular approaches. The second theme involved the key unanswered questions in the control of the cardiovascular system, emphasizing autonomic control, hypoxic vasoconstriction and developmental plasticity in cardiovascular control. The final theme involved poorly understood aspects of the interaction of the cardiovascular system with the lymphatic, renal and digestive systems. Having posed key questions around these three themes, it is increasingly clear that an abundance of new analytical tools and approaches will allow us to learn much about vertebrate cardiovascular systems in the coming years. This article is protected by copyright. All rights reserved.