Others have given examples, but here's one I just did: We have a pellet stove for supplemental heat. Our main system is a heat pump with electric backup - but the heat pump is undersized (thanks, previous owner), so it can't keep up when temperatures get below about 40 degrees (somewhere around there, I forget).

I have an outdoor temperature sensor, and a temperature sensor in the room with the pellet stove. I wired a smart relay controlled by Home Assistant to the pellet stove to act as a thermostat, then defined that indoor temperature sensor and relay together as a thermostat in HA.

Then I wrote this logic:

• If the outside temperature rises above 50, set the pellet stove thermostat to something very low (so it shuts off; the heat pump can handle that just fine).
• If the outside temperature drops below 45, set the pellet stove thermostat to either 70 or 72, depending on whether it's during the night or day.
• Coming soon, once I get around to it: If the HVAC is on auxiliary heat, set the pellet stove to something like 78 degrees, because that will be cheaper than the aux heat.

I'd also like to think about incorporating future info - for example, if the temperature outside is, say, 44 degrees and climbing to above 50 in the next 2 hours, then maybe don't worry about firing up the pellet stove. I may also set something that if it's below, say, 35 degrees outside, then it should keep the pellet stove running no matter what the indoor temperature is.

So here I'm using a Zigbee internal sensor, a 433 mHz outdoor sensor, that smart relay, data from the main HVAC thermostat, and potentially data from forecasts to make my pellet stove operate in a smart, energy efficient manner. HA allows me to take all of this disjoint information and merge it into something useful.

I will likely burn a lot less pellets than I did last year, which also saves me time because I don't have refill the thing as often. The pellet stove will kick on when needed, and shut off when it isn't, and I don't have to worry about it.

Besides, it's kind of fun. ;)