Temptation in the Wilderness
The devil who tempted Christ in the desert certainly need not have been some spiritual demon, as it is usually perceived, but may very well have been a real and living person, one of the descendants of the seed of the serpent who, as Scripture shows in many places, are actually devils.
Temptations
To make stones into Wheat Bread
In the wilderness, Yahshua was tempted by an adversary to make loaves into wheat-bread and responding Christ quoted Deuteronomy 8:1-3 that men live not by bread alone but from every word proceeding out of the mouth of Yahweh. The adversary then tempted Christ concerning his status as a son and quoted Psalm 91:11-12, to which Christ responded explicitly referencing the law of Deuteronomy 6:16 to not tempt Yahweh your God.
To deliberately seek danger for proof of divine protection
It is written that the Messiah will trample over His enemies during the Second Advent in the day of Yahweh's Vengeance. During the temptation in the wilderness, the adversary there attempted to tempt Christ by quoting Psalm 91:11-12 where it says "He commanded His messengers concerning You, and by their hands they shall bear You, lest at any time You may strike Your foot against a stone."
Ironically enough, this adversary failed to quote the proceeding verse which says "“Thou shalt tread upon the lion and adder: the young lion and the dragon shalt thou trample under feet.”
The lion is only an allegory for a strong man, and at Luke chapter 10 verses 18 and 19 Yahshua said "I beheld the Adversary falling as lightning from heaven! 19 Behold! I have given to you authority to tread upon serpents and scorpions, and upon all the power of the enemy, and no one shall by any means do you injustice. “ So we see this same idea conveyed in the Psalm, and the very διάβολος speaking to Christ during the temptation in the wilderness was ironically the subject of that same thing, he himself being a dragon and a scorpion.
"Offering" the kingdoms of the society in exchange of worship
The adversary being a descendant of Cain (and thus having temporary inheritance) then "offered" Christ the kingdoms of the society if he would worship him. Christ responded by quoting "‘Yahweh your God shall you worship, and you shall serve Him only", which is written in a couple of places in Deuteronomy. [ The adversary cannot be the “your” of that scripture, for it is meant to refer to the Israelite receiving the law, and therefore Christ Himself is the subject in this instance.]
The adversary at this time then departed.
Messengers
Following the end of the particular adversary's trial, it is written in Matthew's account that messengers then arrived and served Christ. The “messengers” could refer to angels, or to people of Israel who found Him where the accuser had left Him.
Following Events
It appears that after the ending of the 40 days that Christ had gone to Nazareth to announce His ministry, and then being rejected there as it is described in Luke, he travelled to Capernaum. This appears to be abbreviated in Matthew's account, as John the Baptist is depicted as not having yet been arrested at this time in John's gospel.
Matthew 4:12 And having heard that Iohannes had been handed over [arrested] He withdrew into Galilaia. 13 And leaving Nazareth, having come He settled in Kapharnaoum by the sea in the regions of Zaboulon and Nephthalim,