Who Kalki is
Kalki is the avatar who has not happened yet. Of the ten forms of Vishnu that the tradition counts, nine have come and gone, from the fish to the Buddha or Balarama. The tenth is waiting at the end of time.
The Puranas say that the age we live in, the Kali Yuga, will grow steadily worse. Kings will rob their people, the learned will sell their learning, families will break apart and the rains will fail. When the dark age is at its darkest, Vishnu will be born once more, as the son of a brahmin named Vishnuyasha in a village called Shambhala.
He will be called Kalki. He will learn the arts of war from Parashurama, the avatar who never died. He will be given a white horse, Devadatta, and a sword, and he will ride out across the earth and destroy the wicked, and when he has finished the age of truth, the Satya Yuga, will begin again.
Mleccha nivaha nidhane kalayasi karavalam, dhumaketum iva kim api karalam, Keshava dhrita Kalki sharira, jaya Jagadisha Hare: Jayadeva's verse for the tenth avatar in the Gita Govinda, raising a sword like a comet.
The Kalki Purana, a late text, gives him a whole life story, with a wife, Padmavati, a princess of Simhala, whom he wins with the help of a talking parrot.
Kalki is one of the few gods who is worshipped mostly in hope. His temples are few, and most are recent. But his white horse is in every set of Dashavatara paintings, the last panel, galloping out of the frame.
