This is a tough little perennial (ht 30-60 cm) which hails from China, Vietnam, Taiwan and Japan, and is classified as being in the family Asparagaceae. It grows as an arching clump of shiny, slim, evergreen leaves and is happy to grow in dry, shady spots, although will also cope with some sun - and I have seen it growing in a pond! It is very tough once established. It flowers in February and March, sending up little spikes of tightly clustered bell-like blooms, rather reminiscent of the grape hyacinth, Muscari, which sadly doesn't do very well in our Sydney gardens, but lends its name to this species of Liriope. The most basic form has plain green leaves with purple flower spikes; 'Royal Purple' has very deep purple flowers, and 'Monroe White' has white blooms. They look effective grown with contrasting rounded leaves, such as those of the succulent London pride (Crassula multicava) or any of the ground-covering rhizomatous Begonias. It is excellent used as an edging alongside paths and also looks good in a container. Liriope can even be grown as a kind of rough lawn, if planted reasonably densely, though it can't handle much foot traffic.
There are forms of Liriope with white-variegated leaves, such as 'Variegata'; others (such as 'Gold-banded') have leaves striped with limey-gold, paired with purple flowers, which make a very pretty groundcover in shady places if massed-planted beneath shrubs. To emphasise the variegation in the foliage, place it nearby a plain gold-leaved plant, such as Duranta 'Sheena's Gold' or golden money-penny (Lysimachia nummularia 'Aurea'). It is also attractive grown under the purple form of Plectranthus ecklonii, which often starts blooming in February and also like shade, or its smaller cousin Plectranthus 'Mona Lavender'. Liriope muscari 'Pee Dee Ingot' has all-gold foliage, but doesn't seem as robust as the other cultivars. Liriope muscari 'Okina' has superb white leaves in spring, that become variegated with green over summer, but still remaining very striking: it looks good paired with white flowers or silver foliage.
Liriope muscari 'Samantha' has plump lavender-pink blooms, and looks very effective nestled amongst the groundcover Plectranthus 'Nico', which has purple veins and undersides on its quilted foliage, or the dark purple leaves of Tradescantia pallida 'Purpurea' or stripy Tradescantia zebrina.
'Evergreen Giant' grows to 80cm or more and is an excellent foliage plant in shade, giving the effect of an ornamental grass and providing good foliage contrast to broad-leaved plants such as Clivia, Alocasia, Begonia and bromeliads. It has purple flowers, though these are often hidden by the leaves, which are its main attraction.
All Liriope plants may produce black berries in autumn after the flowers fade. The foliage can become a bit shabby over winter, especially in colder regions, and apparently can be cut off (or even mown over!) in late August and new leaves will grow to replace the old. Just be careful not to damage the plant's dormant crown. Propagation is by division of the clumps. The plants are frost hardy. The plain green forms are the best choice for very dry shade.