Sometimes referred to as "Geothermal" , the ground source heat pump (GSHP) is becoming a common method of heating.

Basic description of the component parts of a GSHP: see photos

1 A heat pump packaged unit: Water-Water (or Brine-Water) type. (approx. the size of a small fridge) containing a pair of cold-water (glycol) and a pair of heated-water connections.
2. The heat source which is usually a closed loop of plastic pipe containing a Glycol Antifreeze solution. This pipe is buried in the ground in vertical bore holes or horizontal trenches. The trenches take either straight pipe or coiled pipe, buried about 1.5 to 2m below the surface. A large area is needed for this.
3. The heat distribution system. This is either underfloor heating pipes or conventional radiators of large area connected via normal water pipes.
4. Electrical input and controls. The system will require an electrical input, three-phase being preferred, but single phase is perfectly adequate for most systems. A specialised controller will be incorporated to provide temperature and timing functions of the system.

This type of installation offers many advantages.

a) The water-water (or antifreeze-water) heat pump unit is a sealed and a reliable self contained unit.
b) There are no corrosion or degradation issues with buried plastic pipes.
c) The system will continue to provide the same output even during extremely cold spells.
d) The installation is fairly invisible. i.e. no tanks or outside unit to see.
e) No regular maintenance required.

Some tips:
The efficiency of any system will be greatly improved if the heated water is kept as low as possible. For this reason, underfloor heating is highly recommended. It is vital to ensure that the underfloor layout is designed to use low water temperatures. i.e. plenty of pipe and high flow-rates since heat pumps have a different design emphasis to boiler systems. A mixing valve to drop the temperature for the floor pipes should not be used.

Many underfloor systems use zone valves. As they close, they reduce the flow-rate. To maintain the correct flow-rate through the heat pump a buffer tank is suggested. If sufficient areas of floor are always-on, then a buffer cylinder may not be required.

If the building is well insulated and mostly open-plan, then separate zones may not be needed. In this instance the buffer tank may not be necessary. A very good underfloor heating layout in a screed is critical to good performance.

If radiators are to be used, they must be large enough. At least double the normal sizing (as used with a boiler) is a good starting point. but they will never be as good as well-designed underfloor heating.
The pipework for radiators should be considered carefully such that the flow is not restricted. high flow-rates are desirable. TRV's are sometimes a hindrance.

The energy efficiency will be significantly better from underfloor heating utilising solid screed (tiled etc) finishes. The running costs will be higher if timber finish, and/or carpets are used.

If your house is not particularly well insulated, then you need to be more careful with the underfloor or radiator design. Poorly insulated houses may not be suitable for full-heating using underfloor heating. These should ideally have tiled surface (no wood and no carpets).

Whilst this type of heat pump installation could provide all the heating needs, it is common practice, and often economic sense, to have a back-up boiler linked to the system to cope with the very cold periods.
Electric back-up is not ideal. This is putting a high load on the mains supply at a time of peak demand. At this time the power station's net fuel efficiency is lower.
Wood stoves are a simple option and good environmentally, but they are labour intensive.

The ground pipe system must be planned carefully, especially since it will be there for well over 50 years. Any mistakes may be too difficult or costly to rectify later. The highest energy efficiency will result from systems that do not go below freezing point, therefore, the bigger the the pipe system/ground area, the better, however, this is costly and a compromise must be sought.
The ground area should be selected carefully. Wetter areas are very much better than dry.
The pressure drop in the pipes should be compatible with standard low-head pumps, and will be calculated by your heat pump expert.

Weather-compensation will significantly improve the annual energy efficiency by reducing the heated water temperature down to the minimum required, dependent on outside temperature. Most heat pumps incorporate this in the controller, if not, then this facility could be retrofitted as an extra.

If you want to keep energy efficiency high, try to keep the heated water temperature as low as possible. Try to keep some zone valves fully open and control the temperature down by carefully adjusting the weather compensation controller. If you don't have weather compensation, simply adjust the water temperature as low as possible such that adequate heating is attained. The setting can be changed throughout the year.

If domestic hot water is provided by the heat pump, you will need a very large heat-exchanger coil within the cylinder, far bigger than boiler fast recovery types. Have a big enough cylinder such that the water can be stored at a slightly lower temperature. Use "thermal store" type systems with caution. They usually require temperatures higher than heat pumps can efficiently provide. That said- this is an topic where there is room for developments and improvements.
Protection from Legionella bacteria must be considered. This often takes the form of an electric heater that is controlled to come on via a time clock.

Heat pump compressors like to run for long periods. Stop-starts should be minimised. Correctly set thermostat differentials and correctly positioned cylinder sensors will all help to maximise run periods .A buffer cylinder will help in many circumstances.,

Noise could be a problem if not considered properly. Be cautious at the design stage and this problem should be eliminated.