This chapter develops a critical analysis of Fundamental Rights Impact Assessment (FRIA). FRIA is a risk-based and ex-ante mandatory procedure for evaluating potential impacts of artificial intelligence (AI) systems that makes an appearance in Article 27 of the AI Act but has not yet entered into force. Nonetheless, it is possible to evaluate it as a distinct type of governance instrument and to understand how it is intended to contribute to AI oversight. FRIA promises to integrate fundamental rights concerns in the cycle of development of AI systems and foster accountability and transparency. The issue is approached by situating FRIA within the broader historical and conceptual landscape of the governance of emerging technologies, with a specific focus on the practice of technology assessment (TA). TA has become a central tool in contemporary governance to evaluate the social, legal and economic consequences of emerging technologies. Drawing on past and current experience in TA, we will examine the methodological and implementation challenges to FRIA, as a tool to produce enhanced knowledge about AI within society and as an effective instrument for steering technological development. Overall, our contribution offers a preliminary evaluation of FRIA, its potential use, and foreseeable challenges. These insights are meant to identify new possible directions for research in legal and social sciences and to improve accountability, transparency and social responsiveness in AI governance.