These spiders, from the sub-order Orthognatha (Mygalomorphae) or primitive spiders, are famous for their falsely suggested "deadly" bites. More about the exaggerated poisonous of these and other spiders can be read here.
The bird-eating spider and Tarantula, which is a common name for these spiders, the Goliath spider (Theraposa blondi) which is the largest spider on the world with a leg span of 30 cm and a weight of 130 grams, Sydney funnel web spider (Atrax robustus)and the mouse spider (Missulena) are names given to species belonging to the order.
In Europe only two members of this sub-order can be found. In Australia 13% (>240) of the spiders belong to the Mygalomorphae.
The ancestral lineage of these spiders goes back over 360 million years.

Most of these spiders live fearful lives buried deep in holes. Many species react on unexpected events by cowering in fear, unable to move, or by violently plunging their pickaxe fangs. (more about the fangs)

The spider can often be spotted when the males start searching for females and leave their burrows. Females are more difficult to find because they can live for several years in their burrow with out leaving it.

The two long spinnerets at the back end of their abdomen and their large fangs that move up and down instead of side ways, like the modern spiders, are characteristic for this order.

Brachypelma smitty (Mexican red knee spider)

Habitat
Their size varies between 15 and 25 mm.
The spiders are similar in appearance as other mygalomorph spiders like the funnel-webs but with very broad heads The common name of the mouse spider is derived from the mistaken belief that this spider excavates a deep mouse-like burrow.
Like the trap-door spiders, the mouse spider lives in burrows in the ground, often in banks of rivers, creeks and other waterways, and is sometimes found in suburban gardens. The burrows are built with double or single trapdoors and the entrance is oval-shaped.
The burrow can extend to a depth of about 30 cm - which is unusually deep for a spider,
but not as deep as previously claimed for this species.
The females tend to remain in or near their burrows throughout their life, and are sluggish
spiders that are rarely aggressive. However Missulena occatoria females have been found to produce copious amounts of highly toxic venom, which is potentially as dangerous as that of the Sydney Funnel-web Spider. A male Missulena bradleyi caused a serious envenomation in a child in the Brisbane region. Males wander during early winter, especially after rain. They will assume a threatening posture if disturbed. Insects are the main prey of mouse spiders.

Distribution
The eastern mouse spider (Missulena bradleyi) lives in eastern Australia from Queensland to Victoria.
The redheaded mouse spider (Missulena occatoria) occurs across most of the mainland, except southern Victoria and northern Australia. The male of this species has a bright red cephalothorax.
The northern mouse spider (Missulena pruinosa) is found in Northern Australia around Darwin.
One species has been described outside Australia in Chile.

Missulena bradleyi Rainbow, 1914; New South Wales
Missulena dipsaca Faulder, 1995; Australia
Missulena granulosa O.P.-Cambridge, 1869; Western Australia
Missulena hoggi Womersley, 1943; Western Australia
Missulena insignis O.P.-Cambridge, 1877; Australia
Missulena occatoria Walckenaer, 1805 ; Southern Australia
Missulena pruinosa Levitt-Gregg, 1966; Western Australia, Northern Territory
Missulena reflexa Rainbow&Pulleine, 1918; South Australia
Missulena rutraspina Faulder, 1995; Western Australia, South Australia, Victoria
Missulena torbayensis Main, 1996; Western Australia
Missulena tussulena Goloboff, 1994; Chile

Missulena occatoria, female red-headed mouse spider Picture by Colin Halliday

Habitat
They are mostly terrestrial spiders, which build typical silk-lined tubular burrow retreats, with a collapsed "tunnel" or open "funnel" entrance from which irregular trip lines radiate out over the ground. Exceptions, which lack trip lines but may have trapdoors, are those Hadronyche from South Australia, like Hadronyche adelaidensis, Hadronyche eyrei and Hadronyche flindersi.
The silk entrance tube may be split into 2 openings, in a Y or T form. In the case of Hadronyche formidabilis the burrow may be in the hollow of a tree trunk or limb, many meters above ground level.
Adult male spiders leave the burrow permanently to seek a mate. Such wandering male spiders may enter houses, sometimes even find their way into clothing, and thus account for many bites. Most funnel-web spiders are ground or log dwellers but at least two are tree dwellers (Hadronyche formidabilis and Hadronyche cerberea: respectively the Northern and Southern tree funnel web spiders).
highlands. Atrax robustus, the Sydney funnelweb spider, has a distribution centering on Sydney, extending north to the Hunter River, south to Shoalhaven River, and narrowing westwards as far as Lithgow.
Hadronyche has a considerably wider distribution; being the coastal areas and highland forest regions from Tasmania to Queensland.

Genus Atrax O.P.-Cambridge, 1877
Atrax robustus O.P.-Cambridge, 1877 ; New South Wales

Genus Hadronyche L.Koch, 1873
Hadronyche adelaidensis Gray, 1984; South Australia
Hadronyche anzses Raven, 2000; Queensland
Hadronyche cerberea L.Koch, 1873 ; New South Wales
Hadronyche eyrei Gray, 1984; South Australia
Hadronyche flindersi Gray, 1984; South Australia
Hadronyche formidabilis Rainbow, 1914; Queensland, New South Wales
Hadronyche hirsuta Rainbow, 1920; New Guinea
Hadronyche infensa Hickman, 1964; Queensland, New South Wales
Hadronyche insularis Rainbow, 1913; Solomon Is.
Hadronyche modesta Simon, 1891; Victoria
Hadronyche pulvinator Hickman, 1927; Tasmania
Hadronyche valida Rainbow&Pulleine, 1918; Queensland,
New South Wales
Hadronyche venenata Hickman, 1927; Tasmania
Hadronyche versuta Rainbow, 1914; New South Wales

Atrax robustus Pictures by Colin Halliday

The Australian Funnel-web spiders (family Hexathelidae, Simon, 1892) are probably the most dangerous spiders we can encounter.
The most famous spider is the Sydney funnel web (Atrax robustus).
Chances to be bitten are small. There are only two cases of envenomation annually in the last 10 years.
Funnel-web spiders belong to the family Hexathelidae and two (Atrax and Hadronyche) of the eleven genera are considered dangerous.

Of the 40 described species in this family, the six red printed species caused severe envenomation.

Misgolas rapax is found around Sydney. Despite their name most Misgolas species, except Misgolas gracilis, do not make a door at the end of their burrow

Misgolas spiders are 15 - 30 mm in length and commonly found in eastern Australia.
The spider can of course bite but the toxin is not dangerous. The penetration of the fangs throught the skin may hurt.

More here from the Australian Museum:

Misgolas rapax Sydney Brown trapdoor spider Picture by Colin Halliday

Unknown Mygalomorph with a length of 15 mm that lived in a dense web on the ground between shrub in Leinster, Western Australia.