I will respond on a "without using mods" basis.
You can check Literacy levels in the Demographics, which will tell you who is the tech leader and who is the tech loser at any given point in time, but it won't tell you what specific techs they have. You can also pay attention to announcements that various civs have entered this or that technological era, but it doesn't tell you what tech got them into that era.
For that you have to use clues. Civ A has built some trading posts -- they have Guilds. Just got an announcement that Civ B has finished Forbidden Palace -- they have Banking. Civ C has knights running around -- they have Chivalry. Once you have a spy, you can see what they have built or are building in their capital (Civ D is building a public school -- they have Scientific Theory).
You get notice that Sweden just entered the Renaissance era -- one of Sweden's Unique Units is the Carolean, which is unlocked with a first-tier Renaissance tech (Gunpowder) -- odds are that Sweden beelined Gunpowder to unlock Caroleans, but you need other clues to verify. Or maybe a spy.
There are other clues you can glean, but that's the thrust of it.