What is the eternal fate of those who died with no knowledge of Jesus Christ?
What is the eternal fate of little children who die before baptism?
What is the eternal fate of the "heathen nations" that never heard of Jesus Christ?
I testify that the atonement of Jesus Christ is for all men. It is for both the living and the dead. It is for those who have never heard His name. It is for little children who died before they were able to accept the gospel and be baptized.
9 For to this end Christ both died, and rose, and revived, that he might be Lord both of the dead and living.
1 Cor. 15:29
29 Else what shall they do which are baptized for the dead, if the dead rise not at all? why are they then baptized for the dead?
How do the dead hear the gospel of Jesus Christ? The scriptures talks about preaching in the spirit world:
1 Peter 3:19
18 For Christ also hath once suffered for sins, the just for the unjust, that he might bring us to God, being put to death in the flesh, but quickened by the Spirit:
19 By which also he went and preached unto the spirits in prison;
Clearly, there must be some reason for preaching the gospel to the dead. If they were lost, if there was no chance for repentance, why preach the gospel to them?
While pondering this scripture, Pres. Joseph F. Smith had the following revelation about this scripture:
Doctrine and Covenants 138:28-34
28 And I wondered at the words of Peter—wherein he said that the Son of God preached unto the spirits in prison, who sometime were disobedient, when once the long-suffering of God waited in the days of Noah—and how it was possible for him to preach to those spirits and perform the necessary labor among them in so short a time.
29 And as I wondered, my eyes were opened, and my understanding quickened, and I perceived that the Lord went not in person among the wicked and the disobedient who had rejected the truth, to teach them;
30 But behold, from among the righteous, he organized his forces and appointed messengers, clothed with power and authority, and commissioned them to go forth and carry the light of the gospel to them that were in darkness, even to all the spirits of men; and thus was the gospel preached to the dead.
31 And the chosen messengers went forth to declare the acceptable day of the Lord and proclaim liberty to the captives who were bound, even unto all who would repent of their sins and receive the gospel.
32 Thus was the gospel preached to those who had died in their sins, without a knowledge of the truth, or in transgression, having rejected the prophets.
33 These were taught faith in God, repentance from sin, vicarious baptism for the remission of sins, the gift of the Holy Ghost by the laying on of hands,
34 And all other principles of the gospel that were necessary for them to know in order to qualify themselves that they might be judged according to men in the flesh, but live according to God in the spirit.
I am thankful for the atonement of Jesus Christ that extends to all men, women, and children; both those living, and those dead. I am thankful for holy temples where we can perform the sacred ordinance of baptism for the dead. The Savior said, "...Verily, verily, I say unto thee, Except a man be born of water and of the Spirit, he cannot enter into the kingdom of God." John 3:5. He gave the commandment that we must be baptized to enter the kingdom of God. I am thankful that He also provided a way to save those who died without the chance.
(Baptismal font, Salt Lake Temple. The oxen represent the 12 tribes of Israel.)