Heat pumps use the air conditioner technology; they can be seen as air conditioners also designed for heating...
Improvements involving multi-stage and variable speed motors are transversal to other heating and cooling equipment. But there are technological developments that are specific to the heat pumps, mostly intended to boost energy-efficiency in cold climates.
Air source heat pumps can be seen as air conditioners specially designed for heating.
Ground source heat pumps (geothermal) can be seen as air conditioners with a long buried coil, moving heat from or to the ground.
This page deals with these issues, and stresses the main technological improvements that you should look for in a new air source heat pump.
Two speed compressors
Two-speed compressors are a major recent advance in the heat pump technology. They can save large amounts of electrical energy and reduce compressor wear. Spiral-shaped scrolls – instead of typical piston compressors – are another recent technological improvement. They provide a quieter functioning and more efficiency in heating mode, besides expending the lifespan of the equipment.
Multi-stage and multi-speed functions
If you are going to buy a new heat pump, prefer a multi-stage model or a similar technology, able to provide flexible heating.
Older heat pump models are single-stage models (On or Off systems). They are unable to respond to modulate their consumption and output to the needs of the building.
New developments make heat pumps smarter in how to use energy.
New heat pumps (including mini-split heat pumps) with special sensors can automatically detect room temperature differences, adjusting their operation for greater comfort and energy savings.
Multi-stage filtration systems can also reduce allergens, besides helping eliminate odors. And they are much quieter than older models...
Mini-split ductless heat pumps come equipped with separate air handlers and thermostats for different rooms (zones). They can provide different heating (or cooling) levels, for different parts of the house.
Cold climate heat pumps & Gas heat pumps
Traditional heat pumps include a set of electric-resistance elements (a sort of giant toasters…) designed to replace the compressor heating cycle when the outside temperature drop down to 35ºF/40ºF (2-5ºC) or less.
These heat pumps become "electric furnaces", consuming large amounts of electricity, and losing their advantage over common electric heaters.
But there are now a new type of air-source heat pumps for cold climates, able to cope with freezing temperatures. These pumps are not fully operational at temperatures as low as say -20ºF, but they are a really great innovation. You just have to take some basic cares when installing and using them (see: Ductless heat pumps).
New heat pumps may come with a small heat exchanger (desuperheater) able to recover waste heat and to use it to heat water. This device can heat water much more efficiently than ordinary electric water heaters.
See: Hot Water Heat Pumps