This section is from the book "An Illustrated Flora Of The Northern United States, Canada And The British Possessions Vol2", by Nathaniel Lord Britton, Addison Brown. Also available from Amazon: An Illustrated Flora of the Northern United States, Canada and the British Possessions. 3 Volume Set..
Annual or perennial herbs, rarely shrubs, with angled striate or terete stems. Leaves alternate or sometimes opposite, exstipulate, simple, entire, toothed or lobed, mostly petioled (in Salicornia reduced to mere ridges). Flowers perfect, pistillate, polygamous, monoecious or dioecious, small,' green or greenish, regular, or slightly irregular, variously clustered, commonly in panicled spikes, bractless or bracteolate, occasionally solitary in the axils. Petals none. Calyx persistent, 2-5-lobed, 2-5-parted or rarely reduced to a single sepal, wanting in the pistillate flowers of some genera. Stamens as many as the lobes or divisions of the calyx, or fewer, and opposite them; filaments slender; anthers 2-celled, longitudinally dehiscent. Disk usually none. Ovary mostly superior and free from the calyx, 1-celled; ovule solitary, amphitropous; styles 1-3; stigmas capitate, or 2-3-lobed or divided. Fruit a utricle, with a thin or coriaceous pericarp. Seed vertical or horizontal; endosperm mealy, fleshy or wanting; embryo partly or completely annular or conduplicate, or spirally coiled.
About 75 genera and 550 species, of wide geographic distribution.
*Embryo annular or conduplicate, not spirally coiled; endosperm copious (except in Salicornia and Kochia).
Leafy herbs; endosperm copious.
Fruit enclosed by or not longer than the calyx or bractlets.
Flowers perfect or some of them pistillate; calyx herbaceous or fleshy. Calyx 2-5-lobed or 2-5-parted; stamens 1-5.
Fruiting calyx wingless, its segments often keeled.
Calyx herbaceous or but slightly fleshy in fruit; flowers mostly in panicled spikes.
Fruiting calyx dry, strongly reticulated; leaves pinnatifid.
Calyx very fleshy and bright red in fruit; flowers densely capitate.
Fruiting calyx horizontally winged.
Endosperm mealy; leaves sinuate-dentate.
Endosperm none; leaves linear, entire.
Calyx of 1 sepal; stamen 1.
Flowers monoecious or dioecious.
Calyx of pistillate flowers none; fruit enclosed by 2 bractlets.
Bractlets flat or convex, not silky.
Bractlets silky-pubescent, conduplicate.
Calyx of both kinds of flowers 3-5-parted; fruit ebracteolate.
Fruit much exserted beyond the l-sepaled calyx; flowers perfect.
Leafless fleshy herbs with opposite branches; endosperm none.
** Embryo spirally coiled; endosperm little or none.
Shrub; flowers monoecious, not bracteolate.
Herbs; flowers perfect, bracteolate.
Fruiting calyx wingless; leaves fleshy, not spiny.
Fruiting calyx bordered by a thin horizontal wing; leaves very spiny.