This is my first time playing Demigod, so I'm in conquest class. The highest level I've won was Monarch.
At the end of the middle ages I had 7 cities on my island and 2 on the island to the west. Babylonians attacked Spanish and razed a city, so I plopped down a city on the ruins. I wanted to expand so I attacked the Spanish (alliance w/ Babylonians). I built up knights, medieval infantry, swiss mercenary, and trebuchet. Research was slow, so I ended up getting most techs from Great Library. I kept trying to take Madrid, but not being very good at war, had a standoff there for many years. Finally I captured the Spanish capital as well as Toledo and 3 cities on the island to the west, which is now entirely mine

. My forces were stretched thin, and Portugal was pulling way ahead in science, so I made peace and built infrastructure, esp. universities and cathedrals.
Explored more, found the Mayans and got communications w/ Aztecs. I was able to build 2 wonders, Sistine Chapel and later Newton's University. To catch up in science I researched Chemistry, which no one else knew, and traded it for Printing Press, Navigation, and Metallurgy, and gpt. I immediately researched Theory of Gravity at 100%. To my dismay the Portuguese, Indians, and Mayans entered the Industrial age ahead of me

. I researched Magnetism and I just finished democracy, so I can switch governments! (I'm in monarchy now)
Madrid culture flipped back to the Spanish, so I declared war again to get it back. I did, but that spoiled my reputation and no one wants gpt from me now!

Indians attacked Egypt and soon almost all the civs allied and joined the fight against Egypt, including me! Indians were taking 1 city per turn, so the whole continent was India before my caravel even got there

(Later I saw how many cavalry they had...) Now the Egyptians are reduced to 1 island city.
Portuguese are really strong, the biggest civ (17% area and population) AND they are furious with us, declaring war on us twice! Fortunately they are too far away to do any real harm, though they do have a powerful navy of carracks. India is gracious to us (fortunately) and first in culture. Mayans are large as well, but not as powerful. Some civs are still stuck in the ancient age! All visible islands have been occupied. (I have a city on island west of Mayans)
1285 AD now. What next? Switch govs, probably research to Medicine (hospitals) then Scientific Method (Theory of Evolution, so I won't fall behind in tech again). I'm trying for diplomatic victory, military victory seems impossible. Hope the other civs like me... (why are they mad at me for attacking the Spanish? They were attacking Spain too!)