For a specific discussion from the link /u/DeSoulis provided, try this one:
https://www.reddit.com/r/AskHistorians/comments/10smgp/why_did_chariot_usage_decline/c6gbioz
A potentially helpful quote:
Horses have gotten big enough not only to carry an armoured warrior, but to be armoured themselves. The only two variants of the heavy chariot left are the scythed chariot with it's very specific role of breaking enemy infantry formations, and what I call the prestige chariot which are ridden by the great kings and important generals.
Unfortunately for the scythed chariot, infantry have been developing too. They're become a lot more disciplined and organised, particularly the Greeks and the Romans, and they learnt a trick that renders even scythed chariots obsolete. When the chariots charge, the heavy infantry open channels to let the chariots through, and supporting light infantry then disable the chariots.
This question has being asked numerous times before, for a list of previous such topics please see:
As mentioned horses got bigger and could support a fully armored fighter. You also need to consider where most of the fighting was taking place, north Africa and the near east, as the civilizations at the time capable of fielding advanced armies where located in this part of the world. Geographically the land around those places is pretty flat, which is good for wheeled vehicles like chariots.
The Persians used a pretty awesome chariot with blades sticking out the side, they would ride into a formation and cut off peoples legs at the knee. Alexander had to deal with these and I think Hannibal used them in the second Punic war.