Cob is a technique with a long unbroken history of use by civilized humans. In its simplest form it is a mix of earth (with sufficient clay) and straw, all wetted down and trodden into a homogenous mass. It is worked into walls usually more than a foot thick. It makes very strong walls due to having the tensional strength of the straw in it. The downside of cob is that without a huge crew of workers it is very time consuming and therefore slow.
It is however virtually indestructible and has the same huge thermal mass as do all earth buildings.
Now here's a popular mostly-new technique!
Straw bale in its current form has only been around as long as bailers have, so the oldest structures are a couple of hundred years old, old enough to prove that it works and can last for a LONG time, if taken care of.
Straw bale is relatively quick and easy, if you are good working with modular construction forms. However, the foundation takes as long as it does for cob, and you can't (enjoyably) live in or really use it for much of anything, until you plaster the walls, which is moderately time consuming. Strawbale really excels at simple, straight walls, when it can be amazingly efficient. On complicated walls (curved, many windows and doors) it is usually better to use another less modular technique, like cob or rammed earth or cordwood.
Also, although it insulates like no other organic material, it does not have the thermal mass of earth or rock, meaning that it will not warm up in the same way as an earth wall exposed to the sun will. Also, unless you have your own bailer you will have to buy bails, unlike earth, which is generally free everywhere.
This one has probably been used since humans have used fire and stacked firewood. The mud it originally used between the sticks has been replaced in more recent times with a masonry/sawdust mix to reduce cracking and provide more insulation.
Cordwood provides a combination of massiveness and insulation, as wood has both these properties. It makes sense if you live somewhere with a lot of suitable firewood trees, and doesn't if you live somewhere with few or no trees.
Compared to log cabin construction, it has the advantage of using small pieces of wood, not weighing more than 20 pounds, and the disadvantage of having to make a great number of cuts.
Here is another unmeasurably old and entirely widespread technique. In its simplest form it involves taking damp (not wet) earth and tamping it into and then onto a wall. Like cob it can be entirely free form, or it can be tamped into a form, giving it uniformity. The most wonderful thing about using earth is that it can be used almost anywhere, as long as the soil has enough clay in it to stick together. \
This is a new technique, invented at Cal-earth out in Southern California. It uses plastic feed-type bags, and the whole uncut rolls of the polypropylene bad material to make earth-filled flattened tubes of soil mixture. It is excellent at making curved or snaking structures and excels at making domes, removing the need for a roof. It also offers the advantage of being able to use a greater range of soil types because the soil is contained within the plastic form. It is generally stabilized with a small percentage of cement. Like cob, the process of mixing the soil (generally using cement mixers) is time consuming and noisy. It is another type of building which is better with more people. Like straw bale, the tubes have to be plastered soon after building or the plastic will photo-degrade in the sun.
Straw and clay can be combined in other ways then just straw bale. One method uses thin upright posts (such as tree branches or split rails) and then weaves bunches of clay slip (watery mud) soaked straw around the poles. Another method uses 2x6 or wider lumber built into walls the same as conventional carpentry, and then stuffs hand fulls of straw soaked in slip in between a temporary plywood formwork, screwed to both sides of the framing. Both of these techniques are plastered after they are built.
Wattle and daub:
Here is another old technique. Popular in medieval Europe as well as a million other places and times. Upright poles have thin flexible material (such as willow shoots or sedge leaves) woven through them. Then the whole thing is of course plastered with may coats until the wall is sufficiently thick.