The Liriope muscari plant (Common name: Big Blue Lilyturf) makes a great plant for borders or also can be planted in mass to create evergreen grassy groundcover.
It has a tufted grass appearance and can easily be grown in most places as it requires very little maintenance.
Photograph by Leonora (Ellie) Enking; Creative Commons.
It is also a great plant to use for areas that suffer from soil erosion.
This plant is a member of the Lirope Plant genus. These are generally known as Lilyturf or Monkey grass, and are typically low growing and grass-like in nature.
As they are evergreens they are often used in gardens as a landscaping plant that can provide year long groundcover.
Photograph by Manuel m. v.; CC.
Liriope muscari is a native of East and, some parts of, South-East Asia and can reach an height of about 18 inches (45 cm).
It grows in clumps and carries dark green strap-like leaves; these are glossy and about 1/2 inch (1.2 cm) wide.
The Lilyturf has compact clumps that slowly expand in spread to about one foot (30 cm). Erect spikes will form and these will bloom with violet coloured flowers towards the end of summer.
One of the reasons that make this a great plant to grow as groundcover is its tolerance to a large array of tough environmental conditions.
It is able to tolerate drought, high humidity, pollution, shade, and soil erosion, and is not usually severely damaged by deer or rabbits.
I recommend this page by Rutgers NJ Agricultural Experiment Station for more information on the best deer tolerant plants to grow in the garden.
There are two main cultivars 'Big Blue' and 'Variegata'.
The first is a slightly taller version of the wild type plant (up to 2 feet (60 cm) with violet flowers.
The second has colourful variegated leaves; these are not as dark a green as the wild-type and have cream coloured edge margins.
Other cultivars include 'Christmas tree' (green leaves, lilac flowers) and 'Lilac Beauty' (lilac flowers); the difference between these two cultivars and normal plants seems to be minimal.