D&C 67

To the elders of the Church, the Lord provides this profound promise -

"...I say unto you that it is your privilege, and a promise I give unto you that have been ordained unto this ministry, that inasmuch as you strip yourselves from jealousies and fears, and humble yourselves before me, for ye are not sufficiently humble, the veil shall be rent and you shall see me and know that I am—not with the carnal neither natural mind, but with the spiritual." (Doctrine and Covenants Section 67:10)

This isn't the only time He has provided such a profound promise. At other times He has said the same thing, noting that each promise has particular conditions -

"And the day cometh that you shall hear my voice and see me, and know that I am." (Doctrine and Covenants Section 50:45)

"...sanctify yourselves that your minds become single to God, and the days will come that you shall see him; for he will unveil his face unto you, and it shall be in his own time, and in his own way, and according to his own will." (Doctrine and Covenants Section 88:68)

And -

"...it shall come to pass that every soul who forsaketh his sins and cometh unto me, and calleth on my name, and obeyeth my voice, and keepeth my commandments, shall see my face and know that I am..." (Doctrine and Covenants Section 93:1)

The Prophet Joseph Smith taught that -

"...after a person has faith in Christ, repents of his sins, and is baptized for the remission of his sins and receives the Holy Ghost, (by the laying on of hands), which is the first Comforter, then let him continue to humble himself before God, hungering and thirsting after righteousness, and living by every word of God, and the Lord will soon say unto him, Son, thou shalt be exalted. When the Lord has thoroughly proved him, and finds that the man is determined to serve Him at all hazards, then the man will find his calling and his election made sure, then it will be his privilege to receive the other Comforter, which the Lord hath promised the Saints, as is recorded in the testimony of St. John, in the 14th chapter, from the 12th to the 27th verses. . . .

Now what is this other Comforter? It is no more nor less than the Lord Jesus Christ Himself; and this is the sum and substance of the whole matter; that when any man obtains this last Comforter, he will have the personage of Jesus Christ to attend him, or appear unto him from time to time, and even He will manifest the Father unto him, and they will take up their abode with him, and the visions of the heavens will be opened unto him, and the Lord will teach him face to face, and he may have a perfect knowledge of the mysteries of the Kingdom of God; and this is the state and place the ancient Saints arrived at when they had such glorious visions—Isaiah, Ezekiel, John upon the Isle of Patmos, St. Paul in the three heavens, and all the Saints who held communion with the general assembly and Church of the Firstborn." (Teachings, pp. 150–51.)

This is what the Lord has promised. The Prophet also taught the process to obtain this great promise -

"We consider that God has created man with a mind capable of instruction, and a faculty which may be enlarged in proportion to the heed and diligence given to the light communicated from heaven to the intellect; and that the nearer man approaches perfection, the clearer are his views, and the greater his enjoyments, till he has overcome the evils of his life and lost every desire for sin; and like the ancients, arrives at that point of faith where he is wrapped in the power and glory of his Maker and is caught up to dwell with Him. But we consider that this is a station to which no man ever arrived in a moment: he must have been instructed in the government and laws of that kingdom by proper degrees, until his mind is capable in some measure of comprehending the propriety, justice, equality, and consistency of the same." (Teachings, p. 51.)

It becomes apparent this promise will not be fulfilled overnight, but in a lengthy testing process of proving worthy.