Not seen any decent pictures or read any professional archeological reports from this site as yet. The best (continually updated), with good pictures, website is possibly here; Amphipolis Tomb Timeline: What We Know So Far About the Magnificent Ancient Greek Monument | GreekReporter.com
Entrance to the tomb.
One of the Caryatids depicting eternal vigilance.
Entrance to the third chamber
Presuming that the dating to the mid to late fourth century is accurate - and certainly the architecture fits from what I have seen - then we are indeed talking Philip/Alexander timeline, the fact that the tomb is considerably larger than that of Philip of Macedon (Alexander's father) suggests it may well have occured after the invasion of Persia and the defeat of Darius.
The million pound/dollar/whatever question is who is it?
Could it be Alexander himself? Very doubtful sadly. His body was seized by Ptolemy and buried in Alexandria by Ptolemy's son. Caesar, Pompey and Octavian/Augustus all saw the tomb in Alexandria in that 1st century AD.
Theodoros Mavraganis, Professor of History and Archaeology in the University of Cyprus, believes it may be the tomb of Hephaestion, possibly Alexander's closest friend and captain of the Companion Cavalry. Hephaestion died in 324 BC at Ecbatana in modern day Iran. It is said that in his grief at Hephaestion's death Alexander imitated Achilles after the death of Patroclus by having all his hair cut off and it has been speculated that had Hephaestion outlived Alexander the Diadochi Wars may not have occured as all would have accepted Hephaestion as successor. Mavraganis says the presence of the caryatids in the tomb may be a reference to Athens - Hephaestion's birth place.
Another theory is that it may be the tomb of Alexander’s Persian wife, Roxana, and his son, Alexander IV who were banished by Cassander to Amphipolis around 310BC and subsequently murdered there or there abouts on Cassander's orders since Alexander's son clearly was a potential threat (in the same way Augustus, Caeser's nephew, murdered Caesar's son (Caesarion) by Cleopatra). Problem with this theory is that a. if you're going to murder Alexander's widow and legitimate son why would you make such a tomb to publicise their murder? b. Frankly Cassander was small fry among the Diadochi only ruling Macedonia and Greece - probably the least powerful of his rival contemporaries. It is doubtful he could have afforded the architecture of such a tomb though certainly the native Greek craftsmen were within his kingdom.
The other theory is that it may be the tomb of the 'admiral' Nearchus who's home was at Amphipolis, although he was born in Crete. After the Diadochi Wars broke out he sided with Demetrius (Antigonus), who killed Cassander's son Alexander V and became Demetrius I of Macedon in 294BC. It is not known where or how Nearchus died but he was reportedly older than Alexander and there is no word of him after 300BC is heard so it is likely he died before Demetrius became King of Macedon so who would have created such a tomb for Nearchus? Not Cassander or his son certainly as they had fought the Antigonids for control of Macedon.
So who is it? Out of all these theories Hephaestion fits best for me. This tomb, it's size and extent, is unlikely to have been made during the Diadochi conflicts when everyone was murdering each other. You don't murder or bury a rival (or an advisor to a rival in the Nearchus case) in such a tomb that must have taken some time to build. Assuming that the caryatids and stone blocks are made elsewhere (there may have also been a stone lion on a large plinth on top of it originally which was found a few kilometres away 100 years ago) just getting the materials to the site and putting them in place, doing the mosaic floor, takes time and money - in other words peace. During the diadochi madness there was less time and money was spent on war and intrigue not to mention the intense rivalry that precluded honouring Roxana/Alexander IV after having murdered them etc... Whoever's tomb it is, or was, the scale and comparative extravagance suggest to me a time of relative stability and a person of immense importance. Of the proposed candidates this fits best with Hephaestion who would have been buried while Alexander still lived.