With respect to the tech tree, today we are clearly in the TH era (this is one of the problems of calling an era "modern", all the other eras are named in a way that is independent of our position in time, but this one is not).
Civ I came out in 1991 and (although its concept of eras was rudimentary) I think that is one of the cornerstones of what we call "modern era" in all civ-like games.
Good point. Naming historical periods is a bit hard as there are several ways of looking at history and there is much overlap. And the various peoples on different continents have different ways of looking at history, from their perspectives.
After the Middle Ages, the most important happening is the growing dominance of the European peoples, up to the beginning of World War 1, when the world basically consisted of European countries, European colonies and European protectorates. This European era also saw a rapid increase in European science and technology. The Chinese and other peoples however view that era as an era of humiliation as they got their butts kicked by European powers.
However the influence of the European peoples are in steady decline mostly due to record low procreation numbers, while many third world countries live in a seemingly unending population boom (*). The current population of the Eu is half a billion people and will continually drop, while the population of Africa will rise from 1 billion at the beginning of this century to an estimated 3-4 billion at the end of this century. In 1900 a third of the world was ethnic Europan while in 2000 this had dropped to 14%, and ethnic Europeans were on average the oldest in the world, the importance being that half the Europeans were past reproductive age, which will mean a further decline in relative numbers in the future. In 1900 there were 3 white persons for every black person in the world, in 2050, this ratio will be reversed. Note that the Roman Empire fell because of steady population decline together with a steady population growth north of its borders, followed by mass migration. A similar situation is now growing with an aging, declining Europe, bordering an Africa and Middle East that have a population boom.
Therefore it is likely that the dominance of the European peoples will end after a few more generation, i.e. somewhere in the later parts of this century, or early next century.
However, while Europe is still at the forefront, ages should be named from a European perspective.
Medieval times
Renaissance (or age of exploration)
Age of enlightenment
Industrial age (ended with WW2)
Atomic age (or post-industrial)
Information age (current age)
Robotic age (near future)
During the Atomic age, people thought the Space age would come after the atomic age. This was at least the view of the science fiction writers of the day. However, as I said elsewhere, the people who went to the moon only brought back rocks, and the mars rover only sent back pictures of rocks, so interest in space colonization has waned. Other than satellites, there is hardly any investment going into space.
Nowadays you can buy a small device, roughly the size of a pack of cigarettes, small enough that you can put it in your pocket, that allows you to instantly communicate with anyone in the world, and gives you access to all the world's knowledge. Much more valuable than having access to more rocks.
Maybe there will be a space age after the robotic age, I don't know. That age will probably be decided by non-European peoples.
(*) see among others, the graphics on
http://ourworldindata.org/data/population-growth-vital-statistics/world-population-growth/
pic 3
which I really don't understand what it means 
ython::tuple {lvalue})
