Angels are beings who have bodies and appear to men in the form of man. (Prophet Joseph Smith, quoted in an Extract from William Clayton’s Private Book, Words of Joseph Smith, Ehat & Cook, p. 44)

There are two kinds of beings in heaven, namely: Angels, who are resurrected personages, having bodies of flesh and bones— For instance, Jesus said: Handle me and see, for a spirit hath not flesh and bones, as ye see me have.  (D&C 129:1-2)

And now, I ask, how righteousness and truth are going to sweep the earth as with a flood?  I will answer.  Men and angels are to be co-workers in bringing to pass this great work, and Zion if to be prepared, even a new Jerusalem, for the elect that are to be gathered from the four quarters of the earth, and to be established an holy city, for the tabernacle of the Lord shall be with them.  (Joseph Smith, TPJS, p. 84)

The enemy that sowed them is the devil; the harvest is the end of the world; and the reapers are the angels. As therefore the tares are gathered and burned in the fire; so shall it be in the end of this world. The Son of man shall send forth his angels, and they shall gather out of his kingdom all things that offend, and them which do iniquity; (Matthew 13:39-41)

“Again, the Kingdom of Heaven is like unto a net that was cast into the sea, and gathered of every kind, which when it was full they drew to shore, and sat down, and gathered the good into vessels, but cast the bad away.”  For the work of this pattern, behold the seed of Joseph, spreading forth the Gospel net upon the face of the earth, gathering of every kind, that the good may be saved in vessels prepared for that purpose, and the angels will take care of the bad.  So shall it be at the end of the world—the angels shall come forth and sever the wicked from among the just, and cast them into the furnace of fire, and there shall be wailing and gnashing of teeth.  (TPJS p. 102)

The Kingdom of God is like a grain of mustard seed.  The mustard seed is small, but brings forth a large tree, and the fowls lodge in the branches.  The fowls are the angelsThus angels come down, combine together to gather their children, and gather them.  We cannot be made perfect without them, nor they without us; when these things are done, the Son of Man will descend, the Ancient Days sit; we may come to an innumerable company of angels, have communion with and receive instruction from them. (Joseph Smith, TPJS, p. 159)

An angel of God never has wings.  Some will say that they have seen a spirit; that he offered them his hand, but they did not touch it.  This is a lie.  First, it is contrary to the plan of God; a spirit cannot come but in glory; an angel has flesh and bones; we see not their glory. (Joseph Smith, TPJS, p. 162)

Many have supposed that the doctrine of translation was a doctrine whereby men were taken immediately into the presence of God, and into an eternal fullness, but this is a mistaken idea.  Their place of habitation is that of the terrestrial order, and a place prepared for such characters He held in reserve to be ministering angels unto many planets, and who as yet have not entered into so great a fullness as those who are resurrected from the dead. (Joseph Smith, TPJS, p. 170)

He [Joseph Smith] explained the difference between an angel and a ministering spirit; the one a resurrected or translated body, with its spirit ministering to embodied spirits—the other a disembodied spirit, visiting and ministering to disembodied spirits.  Jesus Christ became a ministering spirit (while His body was lying in the sepulchre) to the spirits in prison, to fulfill an important part of His mission, without which He could not have perfected His work, or entered into His rest.  After His resurrection He appeared as an angel to His disciples.  Translated bodies cannot enter into rest until they have undergone a change equivalent to death.  Translated bodies are designed for future missions. The angel that appeared to John on the Isle of Patmos was a translated or resurrected body [i.e. personage].  Jesus Christ went in body after His resurrection, to minister to resurrected bodies. (TPJS p. 191)