Heart failure with preserved ejection fraction (HFpEF) comprises almost half of the population burden of HF. Because HFpEF likely includes a range of cardiac and non-cardiac abnormalities, typically in elderly patients, obtaining an accurate diagnosis may be challenging, not least due to the existence of multiple HFpEF mimics and a newly identified subset of patients with HFpEF and normal plasma natriuretic peptide concentrations. The lack of effective treatment for these patients represents a major unmet clinical need. Heterogeneity within the patient population has triggered debate over the aetiology and pathophysiology of HFpEF, and the neutrality of randomised clinical trials suggests that we do not fully understand the syndrome(s). Dysregulated nitric oxide–cyclic guanosine monophosphate–protein kinase G signalling, driven by comorbidities and ageing, may be the fundamental abnormality in HFpEF, resulting in a systemic inflammatory state and microvascular endothelial dysfunction. Novel informatics platforms are also being used to classify HFpEF into subphenotypes, based on statistically clustered clinical and biological characteristics: whether such subclassification will lead to more targeted therapies remains to be seen. In this review, we summarise current concepts and controversies, and highlight the diagnostic and therapeutic challenges in clinical practice. Novel treatments and disease management strategies are discussed, and the large gaps in our knowledge identified.