The Daisy or Aster family was previously known as Compositae and still is in some places.
Mabberely uses Compositae and the Australian National Botanic Gardens uses Asteraceae.

It is the second largest flowering plant family after the Orchidaceae.
There are 1200 to over 1600 genera and 21,400 to over 32,000 species and The Plant List recognises 61,500 synonyms.
Australia has about 1417 native species in 288 genera and up to 300 introduced species that are weeds.
The family can be divided into 24 to 40 Tribes or 5 to 13 subfamilies.
Mabberley recognises 13 subfamilies some with up to 15 sections.

Dividing them into subfamilies:
The Asteroideae subfamily has around 1130 genera and 16,200 species including Cineraria, Senecio,
    Calendula, Ozothamus, Helichrysum, Xerochrysum, Aster, Brachycome, Erigeron, Chrysanthemum
    and Tanacetum.

Carduoideae has around 83 genera and 2,500 species including Cirsium, Cynaria (artichokes), Centaurea, Arctotis, Gazania and lettuce.

The ‘Helianthe Alliance’ has Ageratum, Gaillardia, Coreopsis, Tagetes, Echinacea, Helianthus and Rudbekia.

Mutisioideae has 58 genera and 750 species including Gerberas.

The other subfamilies are Barnadesioideae, Cichorioideae, Corymbioideae, Gochnatioideae,
    Gymnarrhenoideae, Hecastocleidoideae, Pertyoideae, Stifftioideae and Wunderlichioideae.

Many are used as cut flowers and garden ornamentals.
Plants are usually easy to identify as members of the family with their flower heads composed of multiple small florets surrounded by an involucre of bracts, modified sepals, the anthers joined into a tube and an inferior ovary.
Identifying any of the hundreds of small white or yellow ‘daisies’ can be nearly impossible for an amateur.
There are plants in other families with flowers that look like a daisy.

Most members of the family are annual, biannual or perennial herbs.
There are some shrubs, sub shrubs, trees and vines.
In Australia 20% of the natives are shrubs or trees.
Herbs and shrubs can be from 10 cm up to 4 m high, climbers to 3 m long and trees can be over 50 m.
The stems are cylindrical or ribbed, sometimes winged and they often have prickles.
There may be various types of hairs with or without glands and the hairs can be sparse to densely woolly.
Stems and leaves may contain latex and the leaves may be gland-dotted.

Leaves are mostly alternately arranged and in spirals.
Some are opposite or in a basal rosette and they are rarely in whorls.
They are usually on petioles up to 5 cm long sometimes with the blade running down it.
The base of the leaf may have a lobe or auricle on each side that clasps the stem.
The blade may be simple, lobed or up to 3 times palmately or pinnately dissected, trifoliate or compound.
The final divisions may be thread-like giving the leaves a feathery appearance.
The edges may be smooth or toothed and there are often glandular hairs or spines.

Almost all Asteraceae have flowers in a head or capitulum (pl. capitula).
These may be terminal, axillary or leaf-opposed.

An inflorescence can be a solitary head or a variously arranged branched or unbranched cluster (a cyme, raceme, corymb or panicle).
Each head can have a few florets to over 500 in a dense cluster.
The heads may or may not be on a peduncle that can be smooth to densely hairy with simple or glandular hairs.

Flowers are on a receptacle which is an extension of the stem above the level of insertion of the perianth.
It may be flat, slightly convex, conical or columnar.
The surface may be smooth or have depressions that hold the florets.
There are two types of receptacles the paleate and epaleate (without palea).

Palea are scales that may be present at the base of some or all of the florets.
They can be membranous or rigid, with a blunt or pointed tip and may have a hood.
They may have a red or purplish line down them.
There may also be bristles on the receptacle between the flowers and these, with the palea are referred to as the chaff.

Involucral bracts.
The heads are usually surrounded by protective bracts known as phyllaries.
The phyllaries are collectively known as an involucre as it is at the base of a head.

There are 5 to 50 phyllaries in 3 to 5 (1 to 15 or more) series around the base of a head.
Usually spirally arranged they may be free, fused into a cup or overlap like tiles.
They can be lanceolate, oblanceolate, ovate or linear.
They may all be of equal length or the inner or outer whorls may be longer.

Typically they are green and herbaceous but may have a dry papery edge.
Others are all dry, papery and almost colourless while some are coloured.
They may have stalked glands, hairs, prickles or spines.

There are sometimes calyculi which are 1 to 3 series of small bracts around the base of an involucre.

There is almost always a calyx of modified sepals called pappi with the whole calyx being a pappus.
A pappus consists of 2 to 5 (over 100) pappi that may be hairs, awns, scales or fine or coarse bristles.
Their length varies from 4 to 40 mm.
They may be smooth, have barbs, be feathery (plumose) or have hairs with or without glands.
They can be white, almost colourless or brick red, rose, pink, yellow or purplish.

Around any head the pappi may be of a single type but there is often a mix of types.
They are often useful in determining the genus or, more often the species of a daisy.
Rarely there is no calyx.
(The term pappus also refers to the hairs or bristles on seeds.)

A floret is a small flower in a head and it may or may not be on a pedicel.
Each floret may have one or more bracts known as a palea at the base.
The corolla has 5 (3 to 6) petals joined to form a corolla tube with 0 to 5 lobes that are variously arranged.

Ray florets.
A head often looks like a single flower and the ray florets around the edge look like the petals.
They are sessile and may have a one or more palea at the base.
Their corolla tube has a strap-like extension, the ligule or tongue up to nearly 2 cm long.
The long or short tube can have 2 or 3 lobes sometimes with 3 or 2 small lobes or teeth respectively on the opposite side of the tube.
Others have 4 lobes on the ligule and one or none on the rim.
The bilaterally symmetric (bilabiate) ray florets are neuter or females that may have staminodes.

A disk/disc floret is a sessile flower with one or more palea at the base.
It is radially symmetric with 5 (3 to 6) long or (usually) short lobes on the rim of the corolla tube.
They may be the only flowers in a head but typically they form a central disc surrounded by ray flowers.
Disk flowers can be bisexual or unisexual and in various combinations on the heads in an inflorescence.

Filiform florets are peripheral ray florets that have a very slender tube with no ligule or a minute one with
    very small or no lobes. They are usually female.

Ligulate florets have 5 lobes on the ligule.

Petals can be white, yellow, pink, red, orange, blue, purple or brown and may be different colours on each side.
The ray flowers are often yellow and there may be glands on the corolla.
The ray and disc florets are the ones most commonly seen.

Florets may be bisexual, staminate (male), pistillate (female) or sterile (neuter).
These occur in different combinations in the various types of flowers and heads.
The three main types of heads are:

1. Radiate heads have both disc and ray florets.
a.) The outer 1 or more series are bilaterally symmetric ray florets that may be female or neuter.
They usually have 3 lobes on the ligule and together they form the ray.
Some of the florets may be filiform.

b.) The central radially symmetric disc florets are mostly bisexual.
This combination is the commonest type seen in the Asteraceae.
The youngest florets are in the centre.

2. Ligulate heads have only ray florets with 5 teeth on the ligule and they may be bisexual, male or female.

3. Discoid heads. All the florets have radially symmetric corollas with 5 lobes and no ligule and they may be bisexual, male or female.

4. Disciform heads. These have all radially symmetric disc florets with the central ones usually being bisexual or staminate and the peripheral ones female. There may also be filiform and sterile florets but no ray ones.
In an inflorescence some heads may have male and female florets while other heads are all male or all female.

Bisexual florets.
There are usually 5 stamens that alternate with the petals.
The filaments are free and inserted into the corolla tube.
The anthers are usually fused to form a tube around the style and stigma.
The basifixed anthers open inwards via long slits.
There is usually a short appendage on the top of the anthers and sometimes a basal tail that may have
    a fringe or long, soft hairs (plumose).

There are usually scale-like nectaries on top of the inferior ovary.
The ovary of 2 (3) fused carpels and 1 locule has a single ovule with basal placentation.

There is a single apical style that divides into 2 (3) branches that initially lie together low down in the anther tube.
Each branch has a linear stigma on the inner side.
The outer side &/or tip of the branches may have short stiff hairs that collect pollen as the style grows through the anther tube.
When free of the anther tube the style branches separate and present the pollen for pollinators.
The branches may have an apical appendage.

The fruit is a cypsela which is a dry indehiscent single seeded fruit derived from an inferior ovary.
They are commonly referred to as achenes which are similar but from a superior ovary.
They may be cylindrical, flattened sideways, winged or have up to 10 ribs.
There may be a beak at the top sometimes with a ring/s of teeth below it.
The pappus &/or the palea may remain attached and they are sometimes densely woolly.
Burrs have thick barbed apical spines and a few fruit are drupes.