The great challenges faced by modern power systems require a fresh look at the conventional operation paradigm. The significant challenges faced by modern power systems require an innovative method for the conventional operation paradigm. We claim that the decarbonization of the power grid and extensive electrification of numerous sectors of human activity can only be fostered by a self-adaptable and smart power grid that manifests similar qualities to those of the Internet. The Internet is constructed on a layered architecture that facilitates technology innovations and its intelligence is distributed throughout a hierarchy of networks. In this paper, the fundamental differences between the network data flows and power flows are examined, and the basic requirements for an innovative operation paradigm are highlighted. The current power grid is operated in a highly inflexible, centralized manner to meet increased security goals. A new highly flexible, distributed architecture can be realized by distributing the operation responsibility in smaller areas or even in grid components that can make autonomous decisions. The characteristics of such a power grid are presented, and the key features and advances for the on-going transition to a sustainable power system are identified. Finally, a case study on distributed voltage control is presented and discussed.