Artificial intelligence (AI) is the latest trend being implemented in the public sector. Recent advances in this field and the AI explosion in the private sector have served to promote a revolution for government, public service management, accountability, and public value. Incipient research to understand, conceptualize and express challenges and limitations is now ongoing. This paper is the first approach in such a direction; our research question is: What are the current AI trends in the public sector? In order to achieve that goal, we collected 78 papers related to this new field in recent years. We also used a public policy framework to identify future areas of implementation for this trend. We found that only normative and exploratory papers have been published so far and there are a lot of public policy challenges facing in this area, and that AI implementation results are unknown and unexpected; since there may be great benefits for governments and society, but, on the other hand, it may have negative results like the so-called ”algorithmic bias” of AI when making important decisions for social development. However, we consider that AI has potential benefits in the public health, public policies on climate change, public management, decision-making, disaster prevention and response, improving government-citizen interaction, personalization of services, interoperability, analyzing large amounts of data, detecting abnormalities and patterns, and discovering new solutions through dynamic models and simulation in real time.