In this paper, we present a vision of sustainable sixth generation (6G) networks. Sustainability has become inevitable due to the strain on natural resources including materials and energy and increase in greenhouse emissions. The energy consumption and the resulting carbon emissions into the environment will be a serious concern. We cannot expect that the present exponential development will continue because of fundamental limits of nature. We first present a brief summary of system-level principles for future networks. Intelligence will be implemented using feedback loops that should be almost isolated from each other implying loose coupling and fast convergence. We next focus on sustainability challenges, including network management, network security, and network hardware. Several approaches and algorithms are highlighted for the goal-directed distributed network management perspectives of 6G sustainability. Resource consumption in network security can be minimized with enabling sleep mode in idle times, moving towards software-based security functions instead of hardware-based systems, and rethinking of encryption techniques in view of sustainability through code optimization and load fragmentation. High-efficiency antennas can incorporate biodegradable materials to build sustainable network hardware. We also introduce a new research thrust for total control of electromagnetic waves by the modular metasurface antennas making sustainable 6G radio coverage possible in various communication scenarios, e.g., small cell base stations and holographic radio coverage areas.