The spirits of the just are exalted to a greater and more glorious work; hence they are blessed in their departure to the world of spirits. Enveloped in flaming fire, they are not far from us, and know and understand our thoughts, feelings, and motions, and are often pained therewith. (Teachings of the Prophet Joseph Smith, p.325)
[Vision given to Joseph Smith in January 1836 part of which is recorded in D&C 137] Also, I saw Elder Brigham Young standing in a strange land, in the far south and west, in a desert place, upon a rock in the midst of about a dozen men of color, who appeared hostile. He was preaching to them in their own tongue, and the angel of God standing above his head, with a drawn Sword in his hand, protecting him, but he did not see it. (History of the Church, 2:381)
And whoso receiveth you, there I will be also, for I will go before your face. I will be on your right hand and on your left, and my Spirit shall be in your hearts, and mine angels round about you, to bear you up. (D&C 84:88)
They are just as busy in the spirit world as you and I are here. They can see us, but we cannot see them unless our eyes were opened. (Discourses of Brigham Young, p.378)
Where is the spirit world? Is it away up in the heavens? That isn’t what the scriptures and our brethren explain. They have told us the spirit world is right here round about us, and the only spirits who can live here are those who are assigned to fill their missions here on earth. This is the spirit world. And if our eyes could be opened we could see those who have departed from us—a father, mother, brother, a sister, a child. We could see them, and sometimes when our physical senses are asleep, sometimes our spiritual self—and we have ears, spiritual ears, and spiritual eyes—sometimes they will be very keen and awake, and a departed one may come while we are lying asleep and come into our consciousness. We’ll feel an impression. We’ll wake up. Where does it come from? It comes from the spirits of those whom we are sealed to. (The Teachings of Harold B. Lee, p. 58)
I am sure many of you know that the veil can be very thin–that there are people over there who are pulling for us–people who have faith in us and who have great hopes for us, who are hoping and praying that we will measure up–our loved ones (parents, grandparents, brothers, sisters, and friends) who have passed on. (Teachings of Ezra Taft Benson, p.31)
Visitors, seen and unseen, from the world beyond, are often close to us. This is part of eternity which we are living today-part of God’s plan. There is no veil to the Lord. Sometimes actions here, by the priesthood of God, the First Presidency and the Twelve, as we meet in the temple, have been planned and influenced by leaders of the priesthood on the other side. I am sure of that. We have evidence of it. On the other side of the veil, the righteous are taught their duties preparatory to the time when they will return with the Son of Man to earth when He comes again, this time to judge every man according to his works. These righteous spirits are close by us. They are organized according to priesthood order in family organizations as we are here; only there they exist in a more perfect order. This was revealed to the Prophet Joseph. (Teachings of Ezra Taft Benson, p. 35-36)
See President Benson’s story about his mother-in-laws experience with an angel here.