AI is increasingly being implemented in the decision-making process of public administration, from the provision of social benefits to public security policies, generating wide impacts on citizen’s fundamental rights. It is expected that governments’ use of AI will increase the efficiency of public management. Nonetheless, its indiscriminate use is undermining the legality, transparency, and justification of administrative acts. An increasingly necessary question in this new realm is how to guarantee accountability for algorithmic policies implemented by the state. What duties should the public administration assume when implementing AI technologies that impact fundamental rights? Although regulation and practice are still early, algorithmic impact assessments (AIAs) are gaining prominence among academics and policymakers as a key accountability mechanism that should be applied before introducing an algorithmic system in a given context, to prevent its risks, and evaluate its societal implications. Given the importance that AIAs can have for the preservation of trust in government, the rule of law, and fundamental rights, the general aim of this contribution is to explore the fundamentals of AIA, indicating the challenges, stages, and requirements for it to become an effective mechanism for algorithmic accountability by the public administration.