This is an expansive question; as such, I've limited my answer to keep it from getting too much longer. Hopefully someone else can/will address historical interpretations of the imagery.
Ezekiel writes during the time of the exile (1:2) to the people in exile (3:11). Much of Judah has already gone into Babylonian captivity, but at the time he begins writing, Jerusalem still stands. Many of the exiles believed the city would never fall, that it was a sanctuary (cf. 11:3 and 11:11). Against this backdrop comes Ezekiel's prophetic message, which begins with a vision:
The Four Living Creatures
The first thing that Ezekiel recounts of his vision is four living creatures. Later we are told these creatures are cherubim (e.g. 10:20); but in appearance they are a mixture of angel, animal, and human. They have four faces (human, ox, lion, and eagle).
The Great Wheels
Next to each living creature there is a giant wheel made of two wheels intersecting one another. The wheels are covered with eyes. The wheels move in every direction and in unison.
An expanse sits above the heads of the four living creatures, and above the expanse is a throne, and above the throne is a figure of a man gleaming like fire, surrounded by a rainbow-like radiance.
One of the difficulties in interpreting a vision like in Chapter 1 of Ezekiel is the tendency to get lost in the details rather than focusing one's attention on the major ideas. With that in mind, here are a several broad pictures that the vision seems to paint:
The breadth of the expanse and the highness of the throne and the One above the throne suggests the sovereignty of God's rule. Some thought that God has abandoned Israel (9:9), but the vision is to remind its hearers that God is still in control even though the people are in exile.
The four living creatures re-enforce the point above. They seem to represent not only the breadth of God's creation (angel, animal, man), but also the height: each face representing the chief creatures of their domains (man over all creatures, lion over all wild creatures, ox over all domesticated creatures, and the eagle over the birds of the air). All of this sits under the throne (sovereignty) of God.
The brilliance of the light and fire in and around the figure on the throne call to mind the holiness, the majesty, and the glory of God. The rainbow recalls God's promise to Noah and the promise-keeping nature of God.
The many eyes on the wheels likely represent the totality of God's perceiving. Some thought that God did not see what was happening (9:9), but the eyes in Ezekiel's vision show that nothing can escape God's vision.
Lastly, the wheels and the motion of the wheels demonstrate a point critical to the rest of the book: the mobility of God's glory.
This heavenly chariot, as you call it, appears twice more in the book of Ezekiel: once in chapters 10/11 and again in chapter 43. But here it starts by coming from the north (1:4). The north signifies the land of Israel's invaders; judgement comes from the north. As mentioned, many thought Jerusalem was unassailable, but now God gives to Ezkiel a message to deliver: that Jerusalem will be destroyed (Ezekiel 4).
Before that can happen, though, God will leave the city. So in chapter 10, we see again this heavenly chariot and the glory of God departs from the temple and stops above the four living creatures (10:18) and then moves to the east gate. After pausing there, the heavenly chariot moves east of the city altogether to the mountain east of it and Ezekiel's vision ends (11:23-24).
Here is where the mobility of the glory of God becomes important to the theme of the book. For the people thought that God's glory was always in the land and that God was not with the exiles (11:15). The heavenly chariot, though, shows not only that judgement can come upon the land, but also that God is with his people in exile. He has sent them into exile, but He goes into exile with them.
The heavenly chariot, though, makes one last appearance in Ezekiel's book. In chapter 43, Ezekiel sees again a vision like before (43:3) of the glory of God coming from the east (43:2). God returns from the exile, having promised to return the people to the land (36:24). As the rest of the book unfolds, God makes clear that he will not send his people again into exile but that He will dwell with the people he has gathered.