Thy will be done; on earth as it is in heaven.
Augustine of Hippo
When we say: “Thy will be done on earth as it is in heaven,” we pray for ourselves that He would give us the grace of obedience, that His will may be done by us in the same way as it is done in heavenly places by His angels.
John Calvin
43. The third petition is, THY WILL BE DONE ON EARTH AS IT IS IN HEAVEN. Though this depends on his kingdom, and cannot be disjoined from it, yet a separate place is not improperly given to it on account of our ignorance, which does not at once or easily apprehend what is meant by God reigning in the world. This, therefore, may not improperly be taken as the explanation, that God will be King in the world when all shall subject themselves to his will. We are not here treating of that secret will by which he governs all things, and destines them to their end (see chap. 24, s. 17). For although devils and men rise in tumult against him, he is able by his incomprehensible counsel not only to turn aside their violence, but make it subservient to the execution of his decrees. What we here speak of is another will of God, namely, that of which voluntary obedience is the counterpart; and, therefore, heaven is expressly contrasted with earth, because, as is said in The Psalms, the angels “do his commandments, hearkening unto the voice of his word,” (Ps. 103:20). We are, therefore, enjoined to pray that as everything done in heaven is at the command of God, and the angels are calmly disposed to do all that is right, so the earth may be brought under his authority, all rebellion and depravity having been extinguished. In presenting this request we renounce the desires of the flesh, because he who does not entirely resign his affections to God, does as much as in him lies to oppose the divine will, since everything which proceeds from us is vicious.
John Chrysostom
Behold a most excellent train of thought! He bids us to long for the things to come, and hasten towards that day. And he bid us to be earnest in doing here what they do in heaven. For we must long, saith He, for heaven, and the things in heaven; however, even before heaven, He bids us to make the earth a heaven. For there is nothing that stops our reaching the perfection of the powers above here on earth. It is possible act as if we were already in heaven even while abiding here on earth. What these words mean is this: "As in heaven all things are done without hindrance, and the angels are not partly obedient and partly disobedient, but in all things are perfectly obedient; so help us not to do Your will by halves, but perform all things as you will.”
See how He has taught us also to be modest? He has made it clear that we do not gain virtue by our own work only, but also by the grace from heaven? And moreover, He has asked each one of us to take upon himself the care of the whole world. For He did not say, "Thy will be done in me, or in us, but everywhere on the earth."
Cyprian of Carthage
“Thy will be done on earth as it is in heaven.” We do not pray that God should be able to do what He wills, for no one can resist God, but we pray that we may be able to do what He wills. Since the devil hinders us from obeying God with our thoughts and actions, we ask that God’s will may be done in us by God’s help, protection, grace and mercy, since no one is able to do God’s will by his own strength.
We also ask that the will of God may be done both in heaven and on earth because we possess a body from earth and a spirit from heaven so we are earth and heaven. So we pray that God’s will may be done in both our bodies and our spirits. Between our flesh and spirit this is a struggle. Every day they disagree with one another so that we cannot do the good things we want to do. Our spirit wants to do heavenly things, but the flesh lusts after earthly and temporal things. So we ask for God’s help to bring them into agreement so that our soul may be preserved.
And finally, because the Lord commands us to love our enemies, we also pray for those who have not yet begun to be heavenly. We ask that God’s will be done in them. That is we pray that all men would be saved.
Martin Luther
60] Thus far we have prayed that God's name be honored by us, and that His kingdom prevail among us; in which two points is comprehended all that pertains to the honor of God and to our salvation, that we receive as our own God and all His riches. But now a need just as great arises, namely, that we firmly keep them, and do not suffer ourselves to be torn therefrom. 61] For as in a good government it is not only necessary that there be those who build and govern well, but also those who make defense, afford protection and maintain it firmly, so here likewise, although we have prayed for the greatest need, for the Gospel, faith, and the Holy Ghost, that He may govern us and redeem us from the power of the devil, we must also pray that His will be done. For there will be happenings quite strange if we are to abide therein, as we shall have to suffer many thrusts and blows on that account from everything that ventures to oppose and prevent the fulfilment of the two petitions that precede….
65] If we would be Christians, therefore, we must surely expect and reckon upon having the devil with all his angels and the world as our enemies who will bring every possible misfortune and grief upon us. For where the Word of God is preached, accepted, or believed, and produces fruit, there the holy cross cannot be wanting. And let no one think that he shall have peace; but he must risk whatever he has upon earth-possessions, honor, house and estate, wife and children, body and life. 66] Now, this hurts our flesh and the old Adam; for the test is to be steadfast and to suffer with patience in whatever way we are assailed, and to let go whatever is taken from us.
67] Hence there is just as great need, as in all the others, that we pray without ceasing: "Dear Father, Thy will be done, not the will of the devil and of our enemies, nor of anything that would persecute and suppress Thy holy Word or hinder Thy kingdom; and grant that we may bear with patience and overcome whatever is to be endured on that account, lest our poor flesh yield or fall away from weakness or sluggishness."
Martin Luther
The Third Petition. Thy will be done on earth as it is in heaven. What does this mean?--Answer. The good and gracious will of God is done indeed without our prayer; but we pray in this petition that it may be done among us also. How is this done?--Answer. When God breaks and hinders every evil counsel and will which would not let us hallow the name of God nor let His kingdom come, such as the will of the devil, the world, and our flesh; but strengthens and keeps us steadfast in His Word and in faith unto our end. This is His gracious and good will.
"Thy will be done on earth, as it is in heaven." -- Wherever the king of God has come it is the necessary and immediate consequence that his will be done. Wherever God dwells in a soul by faith, and Christ reigns in a heart by love his will is done.
Many people probably imagine that this is merely an expression of resignation, or a request for willingness to suffer the will of God, whatever it may be. This is unquestionably a divine and excellent attitude. It is even a gift of God, but this is not primarily what we pray for in this petition. Instead of a merely passive acceptance we here pray for the strength to actively conform to the will of God.
When we pray that the will of God may "be done on earth as it is in heaven," we ask that all mankind may do the will of God just as willingly as the holy angels do it, and that they may do it continually and perfectly. We also pray that "the God of peace may make all men perfect in every good work to do his will, and work in them all that is well-pleasing in his sight through the blood of the everlasting covenant.
In other words, we pray that we and all mankind may do the whole will of God in all things; and nothing else. We pray that we may do the whole will of God as he wills and in the manner that pleases him. And, lastly, we pray that we may do his will for the sole reason that it is his will.