Origin: Neem (Azadirachta indica) belonging to Meliaceae family, has been an integral part of Chinese, Ayurvedic, and Unani medicines. The Sanskrit name for neem tree is "Arishtha," meaning "reliever of sickness."  In Sanskrit neem is also addressed as “Nimba,” meaning to give good health. 
The first proof of neem being used therapeutically dates back to 4500 years ago. The evidence was unearth from the excavations at Harappa and Mohenjo-Daro in Northwestern and Western India.  Neem discovered from these excavations signal to the fact that it was medicinally used by one of the great civilizations in the ancient world i.e. Indian Harappa civilization. 
One of the most ancient medical system, Siddha dates back to 10 000 B.C to 4 000 B.C. In the records of this age old medicine, the first medicinal plant spoken off is neem.  Bhogar Siddhar, a famed Tamil intellect moved to China to spread the knowledge of Siddha sciences and along with it he spread neem. 
For centuries, Siddha and Ayurvedic doctors have believed neem to be anthelmintic, antifungal, antidiabetic, antibacterial, antiviral, contraceptive, and sedative. One of the earliest references of neem as medicinal plant was uncovered in Thirumular Thirumantiram-Ennayiram, Tholkappiam and ancient Tamil works of Sangam. 
Three hundred and fifty years old palm leaf manuscript conserved in the Centre for Traditional Medicine and Research (CTMR), Chennai, India, titled as Agathiyar Gunavagadam speaks off the therapeutic uses of neem in curing bile disorders, preventing and treating ulcers, CNS disorders, paralysis and psychatric disorders.
Agathiyar Gunavagadam was written by the eminent Siddhar Agathiyar in the 6th century B.C. Soon, neem tree was introduced in Australia, East and sub-Sahelian Africa, South East Asia, and South America. Ayurveda recommends using neem in summers to pacify pitta (one of the doshas). 
Scientifically: Neem leaves are filled with anti-bacterial properties thus helping with infections, burns and other skin problems.  Neem leave benefits are it heals wound healer, helps with anorexia, nausea, belching, dandruff, eye trouble, zits, ear ailments, etc. On the flip side, neem flowers are used to cure anorexia, nausea, belching and intestinal worms. As per a 2008 study, the alcoholic extract in neem flowers works as a great contraceptive. 
Neem oil is rich in healing properties thus is a famous ingredient in cosmetics products such as soaps, hair oil, hand wash, soap etc. Neem twigs are used to cure cough, asthma, hemorrhoids, intestinal worms, low sperm levels, urinary disorders, and diabetes.
Modern science states that 140 compounds from the Neem trees can be used for therapeutic purposes. To name a few polysaccharides, catechin, gallic acid, sodium nimbidate. The mentioned compounds work as anti-inflammatory agents. 
It contains the azadirachtin compound that arms it up with antibacterial, antifungal, and antiparasitic properties.  Neem leaves are packed with the goodness of vitamin C, proteins, calcium, phosphorus, carotene, and fatty acids. As per a research, daily application of neem leaf extract gel to the teeth and gums reduces plaque formation.
Usage: In India, the shoots and flowers of neem tree are consumed as vegetable. In Andhra Pradesh, Karnataka and Telangana, neem flowers are used in Ugadi Pachhadi (soup-like pickle). As per tradition, on the Telugu and Kannada New Year titled as Ugadi day, a small amount of Neem and Jaggery (Bevu-Bella) is eaten. 
During Gudi Padva, the Maharashtran New Year in the state of, a small quantity of neem juice or paste is consumed. In Tamil Nadu, neem plays a significant role in the the Mariamman temple festival. Today, neem is widely used as face pack. 
Below are some DIY with neem: 
- Mix 15 marigold petals powder, 4 neem leaves powder and ½ cucumber and ½ cup coriander leaves powder. Apply it all over. Wash it off after 15 minutes. This is excellent for acne. 
- Take a tablespoon of neem powder and add some water to make a thick paste. Apply this on the face and rinse after 15 minutes. This fights acne and blemishes.
- Take a teaspoon of neem powder, a teaspoon of gram flour and make a paste of it with lemon juice. This helps in removing pigmentation.
- For sebum control, take few neem leaves and blend them with yogurt and lemon juice. Apply this mixture on the face for 15-20 minutes. Rinse later.
- Make some neem paste and add some honey to it. Apply this to face for 10 minutes and then rinse. This helps in hydrating the skin.
- Boil 15-20 neem leaves in water and lets it chill for some time. You can use this concoction as a body rinse after the shower. This helps in getting rid of any skin irritation.