Are there routers in SDN?

Excuse me, could you please clarify if routers are a part of Software-Defined Networking (SDN) architecture? I've heard that SDN is about abstracting the control plane from the data plane, but I'm not entirely sure if routers still play a role in this framework. Do routers still exist and function in SDN environments, or have they been replaced by some other type of forwarding devices? Additionally, if routers are indeed used in SDN, how do they interact with the SDN controller and how does this impact network performance and scalability?