Do smart plugs work when the internet is down?

It depends on the type. Wi Fi smart plugs that rely on cloud servers will lose voice control and remote access during an internet outage, but many retain their programmed schedules locally. Zigbee and Thread plugs running through a local hub (SmartThings, Home Assistant) continue working fully during outages because commands process locally. Apple HomeKit automations also run locally through a HomePod or Apple TV. If reliability during outages matters, prioritize local processing ecosystems over cloud dependent ones.