Heat pupmps are big here in Germany with new builds now but also with old renovation projects.
Your house needs to be insulated to a high standard and preferably have underfloor or wall/ ceiling heating where you need a low output temperature 30 max 40 degrees.
Using heat pumps for normal radiators where you need at least 60 degreas output is very inneficient and probably not worth it.
Heat pumps come in various forms like air heat pumps, water heat pumps, thermal heat pumps.
I´m renovating my house build 1977 with around 200 square metres of space.
At the moment i still have oil heating with 2 x 2000 liter tanks in the cellar. I've got rid of my normal radiators and now have Ceiling heating in every room which need a water heat output temperature of around 37 degrees to keep all rooms at a steady 22 degrees and bathrooms around 24 degrees.
In the next year or so i will be changimg the heating system and will be going for a thermal heating system where the system uses the water from around 100 +/- meters underground (which is around 10 degrees constant all year round).
Will also combine it with solar on the roof to produce leccy to help run the heat pump.
Basically heat pumps are the future :)