Here is another foretelling of the advent of Lord Kalki, the incarnation of Godhead. He is to appear at the conjunction of the two yugas, namely at the end of Kali-yuga and the beginning of Satya-yuga. The cycle of the four yugas, namely Satya, Tretā, Dvāpara and Kali, rotates like the calendar months. The present Kali-yuga lasts 432,000 years, out of which we have passed only 5,000 years after the Battle of Kurukṣetra and the end of the regime of King Parīkṣit. So there are 427,000 years balance yet to be finished. Therefore at the end of this period, the incarnation of Kalki will take place, as foretold in the Śrīmad-Bhāgavatam. The name of His father, Viṣṇu Yaśā, a learned brāhmaṇa, and the village Śambhala are also mentioned. As above mentioned, all these foretellings will prove to be factual in chronological order. That is the authority of Śrīmad-Bhāgavatam.
(Srimad Bhagavatam------1:3:25------purport).

No one, therefore, can be accepted as an incarnation of the Lord if his father's name, as well as the name of the village or place in which he appears, is not mentioned by the authorized scriptures. In the Bhāgavata Purāṇa the name of the Kalkiincarnation, which is to take place in almost four hundred thousand years, is mentioned along with the name of His father and the name of the village in which He will appear. A sane man, therefore, does not accept any cheap edition of an incarnation without reference to the authorized scriptures.
(Srimad Bhagavatam------2:7:2------purport).

The symptoms of such uncultured social animals are already in vogue, and it is the duty of the leaders of men to take note of it and try to reform the social order by introducing the principles of twice-born men trained in the science of God consciousness. This can be done by expanding the culture of Śrīmad-Bhāgavatam all over the world. In the degraded condition of human society, the Lord incarnates as the Kalki avatāra and kills all the demonic without mercy.
(Srimad Bhagavatam------2:7:38------purport).

We can certainly imagine how deteriorated human civilization will be by the end of Kali-yuga. Indeed, there will no longer be a sane man capable of understanding God and our relationship with Him. In other words, human beings will be just like animals. At that time, in order to reform human society, Lord Kṛṣṇa will come in the form of the Kalkiavatāra. His business will be to kill all the atheists because ultimately the real protector is Viṣṇu, or Kṛṣṇa.
(Srimad Bhagavatam------5:12:7------purport).

The Kalki avatāra is the fierce incarnation who vanquishes the class of the atheists born in this age of Kali. Now, in the beginning of Kali-yuga, many irreligious principles are in effect, and as Kali-yuga advances, many pseudo religious principles will certainly be introduced, and people will forget the real religious principles enunciated by Lord Kṛṣṇa before the beginning of Kali-yuga, namely principles of surrender unto the lotus feet of the Lord.
(Srimad Bhagavatam------6:8:19------purport).

This is only the beginning of Kali-yuga, but at the end of Kali-yuga the entire population will consist of mlecchas because no one will follow the Vedic principles. At that time the incarnation Kalki will appear. Mleccha-nivaha-nidhane kalayasi kara-bālam. He will kill all the mlecchas indiscriminately with his sword.
(Srimad Bhagavatam------9:16:33------purport).

The Lord is the maintainer of brahminical culture. His first concern is to see to the benefit of cows and brāhmaṇas. As soon as human civilization turns against brahminical culture and allows unrestricted killing of cows, we should understand that men are no longer under the control of the Vedic culture but are all yavanas and mlecchas. It is said that the Kṛṣṇa consciousness movement will be prominent within the next ten thousand years, but after that people will all become mlecchas and yavanas. Thus at the end of the yuga, Kṛṣṇa will appear as the Kalki avatāra and kill them without consideration.
(Sri Caitanya Caritamrta------1:3:50------purport).