In this review paper, first of all, an analysis of the circular economy and its application to steel structures is carried out. It highlights the need to apply the philosophy of Design for Deconstruction or Design for Disassembly (DfD) from the conception of the structure so that it can be truly reconfigurable. Then, a brief review of the different types of connections for steel structures is conducted, comparing the level of research and development of each of them and the degree of reconfiguration that is possible to obtain. Subsequently, the article focuses on the type of connection using clamps, a key point of this work and on which, to date, there are no state-of-the-art studies. It describes the types of clamps, their principle of operation, the types of connections developed with them, and the results of the different investigations that allow for calculating these types of connections. A summary is also given of how these connection types work according to the geometrical characteristics of the clamp and the bolt so that this review work can serve as a driver for the widespread use of clamp-based connections by researchers and engineers in the design and manufacturing of demountable and reconfigurable steel structures. Finally, some conclusions are given, indicating the advantages and disadvantages of this connection system and future lines of research.