The article introduces the notion of High-Risk AI System (henceforth h-AIS) as per the recently published AI Act (henceforth AIA). h-AIS are the most heavily regulated set of applications under the AIA, that imposes obligations during the design, development, production, deployment and use of said applications. Those rules heavily impact how h-AIS are to be conceived, certified and used, to be lawfully distributed on the European market. The purpose of this article is therefore to (i) provide an understandable explanation of the notion of h-AIS and (ii) of its implications for those intending to develop AIS to be distributed on the European market; as well as (iii) increase awareness about the complexity of that assessment, and (iv) of the need to collaborate with lawyers already in the design phase to ensure compliance with EU regulation.