Renunciation and monasteries (ashrams) play an extremely important part in Hinduism. The sadhus (sanyasis) and sadhvis (sanyasinis) are among one of the most important supporter and promulgator of the Dharma. One of the core teachings of Sanatana Dharma is that all suffering is the consequence of sense‐indulgence (consumerism) and devotion to material and worldly possessions, people and circumstances. It therefore follows that rejection of the material world and consumerism will lead to happiness, and the teaching of renunciation (sanyasa) is one of the pillars of Sanatana Dharma. This sanyas (renunciation) must be a total cerebral act in order to be fruitful, physical renunciation without the mental judgement is a waste of time!
The sanyasis are all those men and women who have rejected the world and all formal religious expression. This means that they no longer carry out rituals on behalf of themselves or others and limit their practices to meditation and study of the Upanishads and Vedas which deal with scriptural and philosophical matters, and the teaching of Dharma. They may be ex‐priests but mostly they are common people from all four castes who have taken to this calling. Some live in monastic centers (ashrams or mathams) and some resides alone and make their living by begging.
When one becomes disenchanted with material life, and decides to reject everything one goes off and take up residence in a monastery (math or ashram). There, after leading the life of a celibate neophyte for seven to twelve years one may take the final vows of a monk/nun and adorn the saffron robe. These vows are irrevocable and taken only after great deliberation. The life of a sadhu/sadhvis is one of dedication to the spiritual path and the pursuit of enlightenment and bliss. All their actions are dedicated to the welfare of all beings.
There is no central ecumenical authority or hierarchy and even the sectarian orders that do exist are more democratic and independent than authoritarian and structured. Most initiated traditional Hindu priests owe loyalty to a monastic seat (Matham or Pitha) and the priest of such a Matham is consulted in matters of pious law and concord but has no authority over the priests.