Xterminator- On Deity the AI starts out with 1 free settler, 2 extra workers, and 12 military units. Plus their growth and production rates are 40% faster than yours (they only need 6 shields to build a warrior that takes you 10 shields, and they only need 12 food to grow vs. your 20).
Plus you only have 1 citizen born content, have no bonus vs barbarians, and have terrible odds on goody huts, while the AI is playing by regent level rules (the AI plays by regent rules, regardless of what level you play) and has 2 citizens born content, better results from goody huts, and a combat bonus vs. barbarians. And they get free unit support. The AI to AI trade rate is also very high. You experience more corruption than lower levels.
On emperor, the AI has a 20% growth/production advantage on you, and they start with 8 military units and 1 free worker. They still have many other advantages, but not as bad as deity.
On monarch, the AI has a 10% growth/production advantage, and 3 free military units. Also some other advantages like free unit support, but not as bad as emperor or deity.
Regent everything is the same except the AI to AI trade ratio gives the AI a slight edge.
And obviously on Chieftain and Warlord, you have a growth/production advantage.
The cost to research is the same for the AI on all levels, but the human is the one that is either shot in the foot or given a bonus. On deity what costs the AI 100 gold to research, would cost you 167 gold (I believe that is the number I have seen) to research yourself, but on chieftain it would cost you only 50 gold.