Walnuts are thought to have originated in the middle east, and have been cultivated by people for lots of years. Years ago it was thought that beating a walnut tree with sticks during harvest encouraged the development of fruiting buds - this ancient belief has been proven false.
In terms of climate and growing conditions, walnuts are moderately fussy but will generally survive anywhere so long as the soil is not too wet (which in turn means not too heavy). However, they will only really thrive if kept well watered (so the soil can't be too sandy or stony either), and in order to crop well they must be protected from strong winds and spring frosts. Wind and frost protection are mainly achieved by planting tall shelter belts around the orchards. In the case of orchards on the Canterbury Plains, with the gentle nor'west zephyr (ha ha - for those of you not in NZ, this is a raging gale-force demon which gives people headaches, incites murder - I kid you not - and dries soil rapidly as well as blowing significant quantities of topsoil into the Pacific), this requires shelter belts to be planted about 3 years ahead of putting in the walnuts, in order to have adequate protection for the vulnerable new growth.
There are numerous walnut cultivars available, and the most recent information is available from the Walnut Industry Group.
Walnuts are not self-fertile (in scientific jargon the term is monoecious) which means that a mixture of trees need to be planted, in order to ensure pollination. Once they are established walnuts don't require too much care, which is appealing. If trained properly in the formative years, they will grow into majestic trees with only moderate attention. In New Zealand there are few pests and diseases, although black rot and walnut blight do occur. Yields are more affected by frost damage, which is a very real risk in Canterbury.
Originating in Europe and West Asia, hazels are a deciduous bush growing up to 6m tall. They are winter flowering and fairly hardy. Also monoecious, about 10% pollinator trees are required. The primary cultivar for the serious orchard is Whiteheart. Markets include processing, baking and confectionery, each with different desired characteristics of nut size and blanching.
The chestnut belongs to the same family as the oak and beech, with the chestnut bur resembling the acorn cup and the chestnut leaf being a longer and more sharply toothed version of the beech leaf. The chestnut is known to have existed in the middle Tertiary period (about 65 million years ago) in Greenland, and fossils have been found in Europe up to 75 million years ago. Chestnuts are monoecious and self-sterile.
North American indians made good use of chestnuts, eating the nuts raw or pounded, or boiled to make a form of doughy bread. The chestnut tree wood is also of value, as is the tannin from its bark. Chestnuts are very popular in Asia and Europe.