1 Peter 4

Peter, speaking of those that not have had the gospel preached to them or had not accepted the gospel comments -

"Wherein they think it strange that ye run not with them to the same excess of riot, speaking evil of you:
5 Who shall give account to him that is ready to judge the quick and the dead."  (New Testament | 1 Peter 4:4 - 5)

Which suggests that even these will have to stand before Christ whether they have received the blessing of the atonement or not.  In that His judgement will be fair, Peter adds -

"For for this cause was the gospel preached also to them that are dead, that they might be judged according to men in the flesh, but live according to God in the spirit."  (New Testament | 1 Peter 4:6)

Thus is obvious, that the spirits of men after they leave this life will continue to have the gospel preached to them -

"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;
20 Which sometime were disobedient, when once the longsuffering of God waited in the days of Noah, while the ark was a preparing, wherein few, that is, eight souls were saved by water."  (New Testament | 1 Peter 3:18 - 20)

It is apparent that after His death on the cross, the Savior brought the message of the gospel to the world of spirits.  In a great vision, President Joseph F. Smith had revealed -

"As I pondered over these things which are written, the eyes of my understanding were opened, and the Spirit of the Lord rested upon me, and I saw the hosts of the dead, both small and great.
12 And there were gathered together in one place an innumerable company of the spirits of the just, who had been faithful in the testimony of Jesus while they lived in mortality;
13 And who had offered sacrifice in the similitude of the great sacrifice of the Son of God, and had suffered tribulation in their Redeemer's name.
14 All these had departed the mortal life, firm in the hope of a glorious resurrection, through the grace of God the Father and his Only Begotten Son, Jesus Christ.
15 I beheld that they were filled with joy and gladness, and were rejoicing together because the day of their deliverance was at hand.
16 They were assembled awaiting the advent of the Son of God into the spirit world, to declare their redemption from the bands of death.
17 Their sleeping dust was to be restored unto its perfect frame, bone to his bone, and the sinews and the flesh upon them, the spirit and the body to be united never again to be divided, that they might receive a fulness of joy.
18 While this vast multitude waited and conversed, rejoicing in the hour of their deliverance from the chains of death, the Son of God appeared, declaring liberty to the captives who had been faithful;
19 And there he preached to them the everlasting gospel, the doctrine of the resurrection and the redemption of mankind from the fall, and from individual sins on conditions of repentance.
20 But unto the wicked he did not go, and among the ungodly and the unrepentant who had defiled themselves while in the flesh, his voice was not raised;
21 Neither did the rebellious who rejected the testimonies and the warnings of the ancient prophets behold his presence, nor look upon his face.
22 Where these were, darkness reigned, but among the righteous there was peace;
23 And the saints rejoiced in their redemption, and bowed the knee and acknowledged the Son of God as their Redeemer and Deliverer from death and the chains of hell.
24 Their countenances shone, and the radiance from the presence of the Lord rested upon them, and they sang praises unto his holy name.
25 I marveled, for I understood that the Savior spent about three years in his ministry among the Jews and those of the house of Israel, endeavoring to teach them the everlasting gospel and call them unto repentance;
26 And yet, notwithstanding his mighty works, and miracles, and proclamation of the truth, in great power and authority, there were but few who hearkened to his voice, and rejoiced in his presence, and received salvation at his hands.
27 But his ministry among those who were dead was limited to the brief time intervening between the crucifixion and his resurrection;
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.
35 And so it was made known among the dead, both small and great, the unrighteous as well as the faithful, that redemption had been wrought through the sacrifice of the Son of God upon the cross.
36 Thus was it made known that our Redeemer spent his time during his sojourn in the world of spirits, instructing and preparing the faithful spirits of the prophets who had testified of him in the flesh;
37 That they might carry the message of redemption unto all the dead, unto whom he could not go personally, because of their rebellion and transgression, that they through the ministration of his servants might also hear his words."  (Doctrine and Covenants | Section 138:11 - 37)