System-of-Systems (SoS) has consolidated itself as a special type of software-intensive systems. As such, subtypes of SoS have also emerged, such as Cyber-Physical SoS (CPSoS) that are formed essentially of cyber-physical constituent systems and Systems-of-Information Systems (SoIS) that contain information systems as their constituents. In contrast to CPSoS that have been investigated and covered in the specialized literature, SoIS still lack critical discussion about their fundamentals. The main contribution of this paper is to present those fundamentals to set an understanding of SoIS. By offering a discussion and examining literature cases, we draw an essential settlement on SoIS definition, basics, and practical implications. The discussion herein presented results from research conducted on SoIS over the past years in interinstitutional and multinational research collaborations. The knowledge gathered in this paper arises from several scientific discussion meetings among the authors. As a result, we aim to contribute to the state of the art of SoIS besides paving the research avenues for the forthcoming years.