This article reviews the three key concepts of modern microwave-filter synthesis using coupled resonators: coupling matrix (CM), extracted pole (EP), and nonresonating node (NRN). CM synthesis is no doubt the most popular and powerful of the three. EP has been around longer as a circuit-synthesis tool, but it seems to have only limited applications. Both CM and EP were developed before the proliferation of electromagnetic (EM) simulators and fast modern computers. CM is widely used because the simple mapping relationship between the physical dimension of coupling structures and synthesized coupling values is well developed. NRN is the newest concept and has drawn a lot of attention. It is a result of circuit synthesis but can also be expressed using CM/EP.