What is the special excellence of Joshua? His generalship, and the distribution of the inheritance, and the taking possession of the Holy Land. (Gregory of Nazianzus, Oration on Basil the Great 43.72)
Everywhere, therefore, he alone kept close to holy Moses amid all these wondrous works and dread secrets. In this way it happened that the one who had been Moses' companion in this intercourse with God succeeded to his power. Worthy surely was he to stand forth as a man who might stay the course of the river, and who might say, "Sun, stand still," and delay the night and lengthen the day, as though to witness his victory. Why? - a blessing denied to Moses - he alone was chosen to lead the people into the promised land. A man he was, great in wonders he wrought by faith, great in his triumphs. The works of Moses were of a higher type, his brought greater success. Either of these then aided by divine grace rose above all human standing. The one rules the sea, the other heaven. (Ambrose of Milan, Duties of the Clergy 2.20.99)
The name of Jesus [Joshua] was a type. For this reason then, and because of the very name, the creation reverenced him. What then! Was no other person called Jesus [Joshua]? But this man was on this account so called as a type, for he used to be called Hoshea. Therefore the name was changed: for it was a prediction and a prophecy. He brought in the people into the promised land, as Jesus into heaven, not the law, since neither did Moses [enter the promised land] but remained outside. The law has not power to bring in, but grace. (John Chrysostom, Homilies in Hebrews 27.6)
But Jesus [Joshua], son of Nave [Nun], was a type of him in many things, for when he began to rule the people, he began from the Jordan; thence also did Christ begin to preach the gospel after he was baptized. The son of Nave [Nun] appoints the twelve to divide the inheritance; and Jesus sends forth the twelve apostles, heralds of truth, into the whole world. He who was the type saved Rahab, the harlot, who had believed; the true Jesus...says "the publicans and the harlots are entering the kingdom of God before you." With but a shout, the walls of Jericho collapsed in the time of the type; and because of these words of Jesus, "There will not be left here one stone upon another", the temple of the Jews just opposite us is fallen; not that this sentence was the cause of its ruin, but rather the sin of the transgressors. (Cyril of Jerusalem, Catechetical Lectures 10.11)
The people of the Hebrews, as we learn, after many sufferings, and after accomplishing their weary course in the desert, did not enter the land of promise until it had first been brought, with Joshua for its guide and the pilot of its life, to the passage of the Jordan. But it is clear that Joshua also, who set up the twelve stones in the stream, was anticipating the coming of the twelve disciples, the ministers of baptism. (Gregory of Nyssa, One the Baptism of Christ)
Jesus (Joshua) of Navi was born of the tribe of Ephraim in Egypt, in the seventeenth century before Christ. When he was eighty-five years of age, he became Moses' successor. He restrained the River Jordan's flow and allowed the Israelites to cross on foot. He caused the sun to stop in its course when he was waging war against the Amorites. He divided the Promised Land among the Twelve Tribes of Israel and governed them for twenty-five years. He wrote the Old Testament book that bears his name, and having lived 110 years in all, he reposed in the sixteenth century before Christ. His name means "God saves."
Apolytikion in the Second Tone
As we celebrate the memory of Thy Prophet Joshua, O Lord, through him we beseech Thee to save our souls.
Kontakion in the Fourth Tone
At thy prayer, the sun stood still, O righteous Jesus; for thou rightly wast adorned both with the likeness and the name of Him at Whose death the sun grew dark. Ever entreat Him to save us who honour thee.