Health technology assessment (HTA) is not simply a mechanistic technical exercise as it takes place within a specific institutional context. Yet, we know little about how this context influences the operation of HTA and its ability to influence policy and practice. We seek to demonstrate the importance of considering institutional context, using a case study of Hungary, a country that has pioneered HTA in Central and Eastern Europe. We conducted 26 in-depth, semi-structured interviews with public- and private-sector stakeholders. We found that while the HTA Department, the Hungarian HTA organisation, fulfilled its formal role envisaged in the legislation, its potential for supporting evidence-based decision-making was not fully realised given the low levels of transparency and stakeholder engagement. Further, the Department’s practical influence throughout the reimbursement process was perceived as being constrained by the payer and policy-makers, as well as its own limited organisational capacity. There was also scepticism as to whether the current operational form of the HTA process delivered ‘good value for money’. Nevertheless, it still had a positive impact on the development of a broader institutional HTA infrastructure in Hungary. Our findings highlight the importance of considering institutional context in analysing the HTA function within health systems.