Hospital-acquired pneumonia (HAP) is pneumonia that occurs ≥48 h after hospital admission; it is the most common hospital-acquired infection contributing to death. Ventilator-associated pneumonia (VAP) arises ≥48–72 h after intubation. Opinions differ on whether VAP is a subset of HAP; the same pathogens predominate in both. Compared with VAP-free controls, patients developing VAP are twice as likely to die and have significantly longer stays in intensive care units. Guidelines recommend that microbiological cultures should guide antibiotic treatment, but these lack sensitivity and take 48–72 h to process, meaning that initial therapy must be empiric, generally with broad-spectrum agents. Given increasing pressure to improve both antibiotic stewardship and patient outcomes, the National Institute for Health and Care Excellence and the Infectious Diseases Society of America recommend research into rapid molecular diagnostic tests to identify causative organisms and their antibiotic resistances. Ideally, these would supersede culture, being quicker and more sensitive. In the UK, the INHALE research programme, funded by the National Institute for Health Research, is exploring rapid molecular diagnostics to inform treatment of HAP/VAP and, given resource implications, incorporates a health economic component. To identify previous economic modelling of HAP/VAP costs to inform this component. Literature review of HAP/VAP studies with economic modelling identified from three databases. Twenty studies were identified. Only one study specifically evaluated strategies to improve diagnosis; the remaining 19 studies omitted this important aspect. HAP/VAP modelling would be improved by better awareness of long-term outcomes and treatment complexity. To the authors' knowledge, no similar literature reviews of economic modelling for HAP/VAP have been published.