The start:

Many Christians believe that the Kingdom of Yahweh will begin when the Son returns in the clouds on His throne. Some believe that it will be when He sits on His throne in Jerusalem.

These are incorrect.

Jesus (Yahushua) said:

Matt.12.28
But if I cast out devils by the Spirit of Yahweh, then the kingdom of Yahweh is come unto you.

Christ had just cast out a devil, minutes before saying this, meaning that the kingdom of Yahweh had already come. This whole episode was about kingdom. Yahushua had been accused of casting out this devil using the power of Beelzebub. But He replied with a discourse about kingdoms. If He cast out the devil, using the power of the devil, then the devil's kingdom would be divided and could not stand. But if He cast it out with the power of Yahweh's Spirit, then He could do that ONLY if the master of the house (Satan) was already bound. In other words, Yahweh's kingdom had already come and Satan's power (and his kingdom) had already been restricted.

When had the Kingdom come?

The wise men knew that the King had been born as Jesus (Yahushua). The wise men wanted to worship Him, as KING. What is a king without a kingdom? Satan's enemy had arrived as the King.

Matthew 2:1,2
Now when Yahushua was born in Bethlehem of Judaea in the days of Herod the king, behold, there came wise men from the east to Jerusalem, Saying, Where is he that is born King of the Jews? for we have seen his star in the east, and are come to worship him.

If the wise men had the ability to know, then Satan also recognized that his enemy had arrived. Satan, afraid of defeat, unsuccessfully tried to use Herod to kill his enemy, the King, but Yahushua and His family had been instructed to flee to Egypt.

The Kingdom had come with the birth of Yahushua, the King, but it had not yet been preached nor was it victorious yet.

Until John the Baptist, the law and prophets ruled. After John, the King ruled His Kingdom and men started entering (pressing) into it. Men couldn't "press into it" if it hadn't yet arrived.

Luke 16:16
The law and the prophets were until John: since that time the kingdom of Yahweh is preached, and every man presseth into it.

Jesus started to preach the Kingdom after John the Baptist was imprisoned.

Mark.1.14,15
Now after that John was put in prison, Yahushua came into Galilee, preaching the gospel of the kingdom of Yahweh, And saying, The time is fulfilled, and the kingdom of Yahweh is at hand: repent ye, and believe the gospel.

"At hand" referred to the victory that was near. Already, Satan's power was waning. Satan was being constrained (bound - Matthew 12:29) allowing the Messiah to be victorious in numerous battles over sickness, death, sin, devils and the minds of men.

The Kingdom was at hand, but the King's final victory was still future. Not very far in the future because Yahushua said:

Mark.9.1
And he said unto them, Verily I say unto you, That there be some of them that stand here, which shall not taste of death, till they have seen the kingdom of Yahweh come with power.

This verse means that the Kingdom would come with power while some were still alive. This would have to be some time less than a hundred years. In fact, it was only three days.

After the last supper Jesus said that He would not eat or drink again until He did it in the Kingdom of Yahweh.

Mark.14.25
Verily I say unto you, I will drink no more of the fruit of the vine, until that day that I drink it new in the kingdom of Yahweh.

Luke.22.16
For I say unto you, I will not any more eat thereof, until it be fulfilled in the kingdom of Yahweh.

Jesus (Yahushua) did eat the same day He was resurrected, after appearing to the two men on the way to Emmaus and returning to Jerusalem:

Luke 24:40-44
And when he had thus spoken, he shewed them his hands and his feet. And while they yet believed not for joy, and wondered, he said unto them, Have ye here any meat? And they gave him a piece of a broiled fish, and of an honeycomb. And he took it, and did eat before them. And he said unto them, These are the words which I spake unto you, while I was yet with you, that all things must be fulfilled, which were written in the law of Moses, and in the prophets, and in the psalms, concerning me.

This verse and the verses preceding, clearly show that the Kingdom had come and ALL things prophesied concerning Him, had been fulfilled. This is the first time that we know for sure that the Kingdom had arrived. Before, it was "at hand" and "near" or "come", but not "all fulfilled".

Yahushua gained the final victory over Satan, over death and over sin. He now rules as King of His Father's Kingdom.

Satan lost the world. Even though he still rules over his own subjects (by their voluntary choice), he no longer is the prince of this world.

Even after this victory, Yahushua preached the Kingdom of Yahweh and predicted the coming great power. This was the power of the Holy Spirit at Pentecost:

Acts 1:3-9
To whom also he shewed himself alive after his passion by many infallible proofs, being seen of them forty days, and speaking of the things pertaining to the kingdom of Yahweh: And, being assembled together with them, commanded them that they should not depart from Jerusalem, but wait for the promise of the Father, which, saith he, ye have heard of me. For John truly baptized with water; but ye shall be baptized with the Holy Ghost not many days hence. When they therefore were come together, they asked of him, saying, Sir, wilt thou at this time restore again the kingdom to Israel? And he said unto them, It is not for you to know the times or the seasons, which the Father hath put in his own power. But ye shall receive power, after that the Holy Ghost is come upon you: and ye shall be witnesses unto me both in Jerusalem, and in all Judaea, and in Samaria, and unto the uttermost part of the earth. And when he had spoken these things, while they beheld, he was taken up; and a cloud received him out of their sight.

The Battles started in earnest at the arrival of the king and His birth. Battles continued until the war had been won. Battles still continue today, even though the war has been won, and they will continue until Satan and his last followers surrender, and are finally thrown into the lake of fire with death itself.

Even though the war has been won and King Yahweh sits on His rightful throne, skirmishes continue. These are battles over the minds of individual men. Even today, you and I have the choice to join Satan as a fallen foe or enter and remain in Yahweh's Kingdom.

The End of the Kingdom:

The Kingdom does NOT last for ever. It will end. The Kingdom was NOT and is not Yahweh's perfect plan. It was not part of His original creation, but was a contingency designed to banish sin and death for ever.

1 Corinthians 15:15-28
Then cometh the end, when he [the Son] shall have delivered up the kingdom to Yahweh, even the Father; when he shall have put down all rule and all authority and power. For he [Yahweh, the Son] must reign, till he hath put all enemies under his feet. The last enemy that shall be destroyed is death. For he hath put all things under his feet. But when he saith all things are put under him, it is manifest that he is excepted which did put all things under him. And when all things shall be subdued unto him, then shall the Son also himself be subject unto him that put all things under him, that Yahweh may be all in all.

The King will set aside His crown and subject Himself to the Father, making the Father all in all. The kingdom is over, the family of Yahweh has been restored so there is no more need of the hierarchical kingdom.

The Father is now Father of all and to all, all in all.