Śrīmad-Bhāgavatam was composed just prior to the beginning of the age of Kali (about five thousand years ago), and Lord Buddha appeared about twenty-six hundred years ago. Therefore in the Śrīmad-Bhāgavatam Lord Buddha is foretold. Such is the authority of this clear scripture. There are many such prophecies, and they are being fulfilled one after another. They will indicate the positive standing of Śrīmad-Bhāgavatam, which is without trace of mistake, illusion, cheating and imperfection, which are the four flaws of all conditioned souls. The liberated souls are above these flaws; therefore they can see and foretell things which are to take place on distant future dates.
(Srimad Bhagavatam------1:3:24------purport).

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).

The cow's milk is required for the sacrificial fire, and by performing sacrifices the householder can be happy. The cow's calf not only is beautiful to look at, but also gives satisfaction to the cow, and so she delivers as much milk as possible. But in the Kali-yuga, the calves are separated from the cows as early as possible for purposes which may not be mentioned in these pages of Śrīmad-Bhāgavatam. The cow stands with tears in her eyes, the śūdra milkman draws milk from the cow artificially, and when there is no milk the cow is sent to be slaughtered. These greatly sinful acts are responsible for all the troubles in present society. People do not know what they are doing in the name of economic development. The influence of Kali will keep them in the darkness of ignorance. Despite all endeavors for peace and prosperity, they must try to see the cows and the bulls happy in all respects. Foolish people do not know how one earns happiness by making the cows and bulls happy, but it is a fact by the law of nature. Let us take it from the authority of Śrīmad-Bhāgavatam and adopt the principles for the total happiness of humanity.
(Srimad Bhagavatam------1:17:3------purport).

The Supreme Lord is so kind to His pure devotees that in proper time He calls such devotees up to Him and thus creates an auspicious circumstance for the devotee. Mahārāja Parīkṣit was a pure devotee of the Lord, and there was no reason for him to become extremely fatigued, hungry and thirsty because a devotee of the Lord never becomes perturbed by such bodily demands. But by the desire of the Lord, even such a devotee can become apparently fatigued and thirsty just to create a situation favorable for his renunciation of worldly activities. One has to give up all attachment for worldly relations before one is able to go back to Godhead, and thus when a devotee is too much absorbed in worldly affairs, the Lord creates a situation to cause indifference. The Supreme Lord never forgets His pure devotee, even though he may be engaged in so-called worldly affairs. Sometimes He creates an awkward situation, and the devotee becomes obliged to renounce all worldly affairs. The devotee can understand by the signal of the Lord, but others take it to be unfavorable and frustrating. Mahārāja Parīkṣit was to become the medium for the revelation of Śrīmad-Bhāgavatam by Lord Śrī Kṛṣṇa, as his grandfather Arjuna was the medium for the Bhagavad-gītā. Had Arjuna not been taken up with an illusion of family affection by the will of the Lord, the Bhagavad-gītā would not have been spoken by the Lord Himself for the good of all concerned. Similarly, had Mahārāja Parīkṣit not been fatigued, hungry and thirsty at this time, Śrīmad-Bhāgavatam would not have been spoken by Śrīla Śukadeva Gosvāmī, the prime authority of Śrīmad-Bhāgavatam. So this is a prelude to the circumstances under which Śrīmad-Bhāgavatam was spoken for the benefit of all concerned. The prelude, therefore, begins with the words "once upon a time."
(Srimad Bhagavatam------1:18:24-25------purport).

The kingdom of God, or the atmosphere of the Vaikuṇṭha nature, which is called the tripād-vibhūti, is three times bigger than the material universes and is described here, as also in the Bhagavad-gītā, in a nutshell. This universe, containing billions of stars and planets, is one of the billions of such universes clustered together within the compass of the mahat-tattva. And all these millions and billions of universes combined together constitute only one fourth of the magnitude of the whole creation of the Lord. There is the spiritual sky also; beyond this sky are the spiritual planets under the names of Vaikuṇṭha, and all of them constitute three fourths of the entire creation of the Lord. God's creations are always innumerable. Even the leaves of a tree cannot be counted by a man, nor can the hairs on his head. However, foolish men are puffed up with the idea of becoming God Himself, though unable to create a hair of their own bodies. Man may discover so many wonderful vehicles of journey, but even if he reaches the moon by his much advertised spacecraft, he cannot remain there. The sane man, therefore, without being puffed up, as if he were the God of the universe, abides by the instructions of the Vedic literature, the easiest way to acquire knowledge in transcendence. So let us know through the authority of Śrīmad-Bhāgavatam of the nature and constitution of the transcendental world beyond the material sky. In that sky the material qualities, especially the modes of ignorance and passion, are completely absent. The mode of ignorance influences a living entity to the habit of lust and hankering, and this means that in the Vaikuṇṭhalokas the living entities are free from these two things. As confirmed in the Bhagavad-gītā, in the brahma-bhūta [SB 4.30.20] stage of life one becomes free from hankering and lamentation. Therefore the conclusion is that the inhabitants of the Vaikuṇṭha planets are all brahma-bhūta living entities, as distinguished from the mundane creatures who are all compact in hankering and lamentation.
(Srimad Bhagavatam------2:9:10------purport).