Synthesis centers offer a unique amalgam of culture, infrastructure, leadership, and support that facilitates creative discovery on issues crucial to science and society. The combination of logistical support, postdoctoral or senior fellowships, complex data management, informatics and computing capability or expertise, and most of all, opportunity for group discussion and reflection lowers the "activation energy" necessary to promote creativity and the cross-fertilization of ideas. Synthesis centers are explicitly created and operated as community-oriented infrastructure, with scholarly directions driven by the ever-changing interests and needs of an open and inclusive scientific community. The last decade has seen a rise in the number of synthesis centers globally but also the end of core federal funding for several, challenging the sustainability of the infrastructure for this key research strategy. Here, we present the history and rationale for supporting synthesis centers, integrate insights arising from two decades of experience, and explore the challenges and opportunities for long-term sustainability.