Helicobacter pylori is an important human pathogen, associated with a substantial burden from both malignant and non-malignant diseases. The bacterium is classed as a human carcinogen, being strongly linked with gastric cancer, the third most common cause of cancer death worldwide and is also associated with common conditions such as dyspepsia and peptic ulcer. Eradication of H. pylori reduces the incidence of gastric cancer and peptic ulcer, as well as the prevalence and costs of managing dyspepsia. Economic analyses suggest that eradication of H. pylori as a means of controlling gastric cancer is cost-effective in high-risk populations. Even in populations at low risk of gastric cancer, there might be other benefits arising from screening and treatment, owing to the effects on non-malignant upper gastrointestinal diseases. However, public health authorities have been slow to consider the benefits of population-based screening and treatment as a means of reducing the morbidity and mortality associated with the infection. There are also concerns about widespread use of eradication therapy, including antimicrobial resistance and a rise in the prevalence of diseases that are negatively associated with H. pylori, such as GERD, Barrett oesophagus, asthma and obesity. This Review summarizes these issues.