There is an emerging interest in heart failure with preserved ejection fraction (HFPEF) because of its high prevalence in the community and several specific characteristics compared with "classic" heart failure with reduced ejection fraction. HFPEF patients are older and more often female, and lack left ventricular dilatation. A likely principal cause of HFPEF is diastolic dysfunction, particularly ventricular stiffening; however, the clinical phenotype of HFPEF is also modulated by dysfunction of other organs such as kidney, vasculature, etc. Despite its social burden, the diagnostic criteria and therapeutic strategies remain to be established. In particular, the lack of established diagnostic criteria has resulted in conceptual confusions about HFPEF in clinical practice. In this review, what is known and unknown about HFPEF is discussed, and several challenging proposals about its diagnosis and therapy are raised.