The EU part
In the EU, with our more central heating system setups, and close to no air condition, heatpump systems are on the comming since a few years.
Heatpumps here are considered low temperature heating systems. They only work with low temperature heat transfer systems (you know, floor\wall\celing heating, heating water in them can be as low as 100°F and still keep it completly warm), though with newer units, a kind of hybrid setting is possible. In the early days, warm water maxed out at 120°F, but by now, all systems I know are capable of 140°F and above.
We have 3 mayor heat sources for our heatpump units.
First is geothermal. Depending on heating size, between 2 and 8 holes anywhere from 30 to 300 feet depth are drilled. Each hole is about 2-8k€.
Specialized coils are the cemented into those holes, pulling heat from the ground.
They are hooked up to your heatpump, which then heats up water for heating and warm water.
The holes are pretty damn expensive (we would have needed 3 holes each about 240ft deep for our house of about 3000ft² only for heating and due to our wish for warm water beyond 100°F we'd needed a 4th hole, comming in at 15k€ for the holes). They only can be used 20 years at max. Further, the needed heatpump cost another 15k€ including installation. These units pull like 5kW and put out between 15-20kW heating power.
The second most common alternative are air heatpumps.
Pretty simmilar to your air heating units, but at sizes of 12-20kW heating output as well, used for hot water and heating. Slightly less expensive with only the unit costs of 15k€, but less efficent at 5kW upward unit size. These things are big, loud and sometimes high maintenance. We have 2 relevants who have 2 different houses, and even though they only pay about 100€ to 200€ a month worth of electricity (thats 1000-2000€ a year versus 3k€ for our oil), they say due to the service cost and the problems with noise, they think it's not worth the saveing against the geothermal version.
The third, and only rare option I know of, are flat area collectors. They are burried 1-2m below the frost level of the soil and spread out about the size of your living area. They work pretty simmilar to the geothermal solutions, but are about half to install. They are slightly less efficen then the air units, but can theoreticly last twice as long as the geothermal units. But they never really cought up.
There have been some new fancy ideas (like a system that uses a tank filled with water that is several thousands of gallons big, about 2 common swimming pools, and a heatpump drawing heat from it, but a solar panel system to put thermal heat back in; during winter, the system slowly retracts the heat from the system, using the additional energy released by the water transforming to ice; being quite rare, incredibly expensive and not quite tested), but even the usual heatpumps are only really effective in new ultra efficent houses and due to high electricity costs not quite a lot cheaper to run otherwise. And they are complicated, hard to service and if so, expensive.
For example, automated wood pellet heating often is cheaper to run.
Just to give you a view in German heating systems.
