As a young man in Massachusetts, Luther Burbank loved the wild oxeye daisies (Leucanthemum vulgare), considered a noxious weed by the local farmers. When Burbank moved to California in 1884, he began developing his nursery and refining the oxeye. After 15 years of breeding, Burbank finally developed an entirely new species, Leucanthemum x superbum, which became an instant success. One simple formula explanation I saw was this: oxeye daisy + English field daisy pollen + Portuguese field daisy pollen + Japanese daisy pollen = Shasta daisy. The true Shasta does not have the invasive characteristics of the common oxeye but if allowed to set seed, some seeds may revert.
The name ‘Shasta Daisy’ supposedly comes from Burbank comparing the crisp white petals to the pure white snow on Mt. Shasta. I have read that the word ‘Daisy’ came from ‘Dad’s Eye’ and morphed into ‘Day’s Eye’ for the similarity of a daisy to the yellow sun with its white ‘rays’.
Shasta Daisies are hardy in zones 4-9 and often characterized by an unusual and somewhat unpleasant odor. They like full sun and well-drained fertile soil with a pH from 6.1 to 7.8 (slightly acidic to slightly alkaline). They tolerate a range of conditions including partial shade but not wet feet in winter. Deadheading extends the blooming season. They are attractive to bees and butterflies but fortunately, not to deer. Propagation is by cuttings or division of the clumps (which should be divided every 2-3 years for plant vigor).
Shastas are best planted in spring after frost has passed, or early fall. When planting from nursery containers, carefully remove the root ball and check to be sure they are not root-bound. I carefully loosen any roots encircling the rootball. Place in well-composted soil, and water well until established.
The first named Shasta daisy developed by Burbank was ‘Alaska’. Later he crossed that with a wild daisy-like Northern California flower to make a double/triple fringe-petalled variety he named ‘Marconi’ and a triple-quadruple petalled variety ‘Esther Read’. There have now been over 100 named varieties introduced since 1901. .
My favorite Shasta daisy is Leucanthemum x superbum 'Becky', discovered growing in Atlanta by Ida Mae Gatlin and passed on to her daughter and then to Jimmy and Becky Stewart. This passalong daisy went through a couple of other people and names before Bill Funkhouser joined Wayside Gardens and included it in their catalogs as Leucanthemum 'Becky'.  Unlike many Shasta daisies, ‘Becky’ will stand up to both the hot, humid Atlanta summers and cold northern winters. The tall stems are strong and do not need staking, and 'Becky' starts blooming late June to early July when other Shastas are finishing.
Some Shasta Daisy Varieties:
Leucanthemum x superbum 'Alaska', 18-30”
Leucanthemum x superbum 'Becky', 36-48”
Leucanthemum 'Broadway Lights', flowers opening bright yellow and turning all shades from butter to cream to pure white as they mature, 18-24”
Leucanthemum x superbum 'Crazy Daisy', early bloomer, fluffy double flowers
Leucanthemum x superbum 'Little Princess', compact 6-12”
Leucanthemum superbum 'Silver Princess', dwarf 12-15”
Leucanthemum 'Snowdrift', shaggy double and semi-double 30-34”
Leucanthemum x superbum 'Snow Lady', dwarf Shasta with 2-3" white flowers, 8-12”
Leucanthemum x superbum 'Summer Snowball', large, double dahlia-like flower heads of pure white with no yellow center, 24-36”
Leucanthemum x superbum 'Switzerland', Multiple flowers per stem, one of the longest bloomers, 24-36”
Leucanthemum x superbum 'Thomas Killen', Extra large single flowers with double rows of white petals, and a crested gold center. Because of its thick, sturdy stems, this variety is better suited as a cut flower. 12-30”
 Bob Hornback, 2001, for The Burbank Shasta Daisy Garden http://www.wschs-grf.pon.net/daisiesetc.htm
Photo Credits: Thanks to hczone6, peachespickett and Victorgardener for their photos from Plantfiles. http://davesgarden.com/guides/pf/go/57377/ The seedling photos are my own, Darius Van d’Rhys.