In Europe we mostly use these "split system" air conditioners, which have a noisy external unit and a more silent internal unit. These air conditioners use a heat pump to move heat from the internal unit to the external unit, and vice versa. They do it by circulating a special liquid/gas in a way that creates high pressure on one side, and much lower pressure on the other. This pressure difference allows the AC system to dissipate heat taken from inside, even if the temperature outside is higher. Thanks to this system the AC is also capable of taking moisture out of the air and let it drip out outside through a tube.
So, long story short, an AC system uses electricity to MOVE HEAT, but doesn't actually create heat, except for a couple of Watts, wasted by the ~90% efficient electric motors used in the fans and compressor... which may add up to about 100W total heat generated (like an average laptop computer or classic light bulb), when operating at full capacity, ~1000W/room power consumption. This is why it's both economical and environmentally friendly to use the AC unit for heating too. Not only does it NOT create any pollution, but also has an average 350% efficiency, meaning that by using 1000W of electricity it brings in (or takes out) 3500W of thermal energy. When you burn wood or natural gas you can only get about 90% efficiency (up to 120% with some advanced burners) and a lot of toxic fumes. Traditional electric heaters don't emit anything harmful, but are also bound by the laws of physics to under 100% efficiency, as they use the electricity to CREATE HEAT.
These split system
ACs cost about 500USD/room and are very practical in places, where you don't have air ducts for a centralized AC system. All the split system AC needs for installation is a small hole in an exterior wall, through which the two 4/3" tubes and a couple of power cables can pass.
... and of course a few screw holes outside and inside to mount the units.