Short answers, pulled from the story.
Vaishnavism is the largest denomination within Hinduism, centered on the devotion of Vishnu as the supreme being and his avatars. A 2020 estimate by the World Religion Database, hosted at Boston University's Institute on Culture, Religion and World Affairs, put the number of Vaishnava Hindus at approximately 399 million.
Vaishnavism originated through the gradual merger of several regional non-Vedic devotional cults between roughly the 7th and 4th century BCE in northern India. These included the Vāsudeva-Krishna cult of the Vrishnis, the Gopala-Krishna traditions of the Abhiras, and the Narayana worshippers. They were identified with the Vedic deity Vishnu in the early centuries CE.
The Alvars were twelve Tamil poet-saints of South India who appeared between the 5th and 10th centuries CE. They composed devotional hymns in praise of Vishnu and Krishna, which were compiled as the Naalayira Divya Prabandha, or 4000 divine verses, by Nathamuni in the 10th century. Their work established bhakti as a path to salvation open to all, regardless of caste.
The avatar doctrine holds that Vishnu descends into the world in material form to destroy evil and restore cosmic order whenever righteousness wanes. The Bhagavata Purana enumerates twenty-two avatars of Vishnu, including Rama and Krishna. The Dashavatara, a ten-avatar scheme, is a later elaboration of this concept.
The four principal Vaishnava sampradayas are the Sri Sampradaya founded by Ramanuja, the Brahma Sampradaya founded by Madhvacharya, the Rudra Sampradaya associated with Vallabhacharya, and the Nimbarka Sampradaya founded by Nimbarkacharya. They emerged in the early centuries of the 2nd millennium CE and differ in their philosophies, ranging from Ramanuja's Vishishtadvaita to Madhva's Dvaita to Vallabha's Shuddhadvaita.
A. C. Bhaktivedanta Swami Prabhupada founded the International Society for Krishna Consciousness in 1966, spreading Gaudiya Vaishnavism to North America, Europe, Africa, Russia, and South America. An earlier pioneer, sannyasi Baba Premananda Bharati (1858-1914), founded the Krishna Samaj society in New York City in 1902 and built a temple in Los Angeles.