I'd start with gen 0, which featured all kinds of goofy operating systems, magazine placement, etc (think broom handles, lugers, borchart, etc) along with complicated assembly/disassembly. These guns were the proof of concept for what would follow.
Then I'd call gen 1 the age of the steel frame, basically starting with the 1911 and it's immediate precursors. Reliable, simple, effective handguns. Due to materials and manufacturing technologies, they are hard/expensive to make today, but these guns were revolutionary, and while obsolete, are not "that" obsolete. Still perfectly serviceable firearms. I suppose I'd put other guns like the higpower here, though you could arguably call it a new generation for the doublestack magazine. While still expensive to make and sharing a lot in common with the 1911, it is essentially the dawn of the modern wonder 9. I would also throw in the CZ75 and similar pistols.
In my opinion, nothing has really changed since the Browning hipower and 1911 as far as the basic operation of the pistol. Even the evolution of striker fired guns dates way back. IIRC, the original prototype hipower was striker fired. I would say the main advancement for "gen 2" is materials science and manufacturing technology. We can now make guns that are as reliable as well built guns of yesteryear every single time, cheaply. I'd put the Glock 17 as one of the founders of this generation. I might also put aluminum framed guns in this category. The basic mechanics are the same operating principles as the 1911.
I think gen 3 is the ability to put reliable optics, flashlights, lasers, etc on the guns.