If we could just heat our homes for free, the problem of a heat source would be solved. However, the cost of heating a home is a two-sided problem. The first is to heat the house for the least economical cost. Next, comes the need to heat the house for the least environmental cost. Both are important.
If financial considerations were the only problem, a house could just be heated with soft coal that produces huge amounts of smoke and pollution. There really is not a much cheaper source of heat. Unfortunately, this type of coal also has one of the highest environmental costs. In cities, the smog created by this type of heat would turn lethal within a few weeks or months.
If the environment were the only factor, we could all use solar energy panels to generate electricity to heat the home. The problem is that panels large enough to produce the kind of power necessary would cost more than the house in some cases. This does not include the cost of batteries and passive heating systems to store energy for cloudy days and at night.
The result is that a blend of the two problems has to be found. A financially feasible heating source that is not too damaging to the environment. Obviously, the old standbys of natural gas, electricity, propane, and heating oil are not in this mix since the idea is to find alternatives.
The first alternative is to return to a source that for centuries was the primary heat source. Install some way to burn wood. With a good air tight system, pollution is minimized, and the source is renewable. The byproduct of ash can be recycled for use in fertilizer and soap. Wood is relatively cheap to use in a well-built energy efficient house. With exterior furnaces and underground heat ducts, the risk of fire in the home is minimal.
In areas where there is large quantities of wind, a wind farm might be installed to generate electricity to offset some if not all of the needs for heating. The problem here is the cost of installation and maintenance. If you are not able to do the labor and technical end of this on your own, the cost could easily become prohibitive.
Ground-based heat pumps have been around for a couple of decades, but have not really gained a great deal of acceptance. The problem is the huge quantities of water needed to make them work. The idea here is to pump the water through buried tubes to heat it to roughly 60 degrees by pulling the heat from the earth. This is the same way that caves stay 60 degrees. When the water is returned to the system, it needs to be only heated a few degrees to make it warm enough to heat your house. This lessens the amount of energy needed to provide heat.
Passive solar is an economical way to go. Glass panels installed on the roof have tubes with water flowing to be heated by the sunlight. Some systems use panels under the glass as conduits for the water to run down and return to collection tubes. The heated water passes down through the walls to a reservoir under the house where it is recirculated back for heating again. The warm water in the walls heats the house. Some systems get a little more sophisticated than this.