A few are powered by mains (I have a habit of using them to automate "dumb" appliances. So I put one in a cheap dehumidifier in place of the physical on switch), and the rest with repurposed small lithium ion rechargable batteries meant to be used with drones.

The battery powered ones need to be careful with how they sip power, but in most cases I can rig something up to get them to last. And the batteries I got off eBay all came with their own USB charger, so like 30 minutes of charging every few months and they are good.

I want to look into solar, but I just haven't had time to tinker with it yet.