Optimising treatment outcomes for people living with hepatitis B virus (HBV) is key to advancing progress towards international targets for the elimination of viral hepatitis as a public health threat. Nucleos/tide analogue agents (most commonly tenofovir or entecavir) are well-tolerated and suppress viraemia effectively in the majority of those who are offered therapy. However, outcomes are not consistent, and we explore the factors that may contribute to incomplete therapeutic responses. We discuss situations in which therapy is not accessible, affordable or acceptable, reflecting the impact of social, cultural and economic barriers, stigma and discrimination, low awareness, poor access to health systems and comorbidity. These challenges are amplified in certain vulnerable populations, increasing the risk of adverse outcomes—which include liver cirrhosis and hepatocellular carcinoma—among people who already experience marginalisation and health inequities. We also tackle the physiological and biological mechanisms for incomplete virological suppression in individuals receiving HBV treatment, considering the possible impact of inadequate tissue drug levels, poor drug–target avidity and genomic resistance. These factors are interdependent, leading to a complex landscape in which socioeconomic challenges increase the challenge of consistent daily therapy and set the scene for selection of drug resistance. By putting a spotlight on this neglected topic, we aim to raise awareness, prompt dialogue, inform research and advocate for enhanced interventions. As criteria for HBV treatment eligibility relax, the population receiving therapy will expand, and there is a pressing need to optimise outcomes and close the equity gap.