ZDOOM AND DERIVATIVES

The official website of ZDoom describes what this source port does fairly well:

ZDoom is a source port for the modern era, supporting current hardware and operating systems and sporting a vast array of user options. Make Doom your own again!

The main draw that makes ZDoom a popular choice for many is that, unlike Vanilla and Boom variants that attempt to preserve the gameplay of the original DOOM, right down to many of its inconveniences, ZDoom is absolutely no-holds-barred on modding possibilities - the engine gets its name from having a proper Z-axis (e.g. the original Doom "fakes" 3D, resulting in the visually odd behavior that monsters and players are infinitely tall, whereas actors can fly over each other in ZDoom), allowing things like slopes and 3D floors in maps (basically floor-over-floor mapping).

Sporting two scripting languages for modders to play around with, the history of ZDoom is rife with mods that not just re-invented how people can play the game, both with crazy maps that look like something out of the Quake engine, and with gameplay mods that can provide new twists on old maps. ZDoom is also fully Boom-compatible, which means every single map from the Vanilla and Boom mod lists works in the ZDoom family.

However, the lead developer of ZDoom retired from the project, officially discontinuing the "main" ZDoom branch. The last release, 2.8.1. was in 2016, and can be found here. However, another branch has continued the path: GZDoom.

GZDoom's main draw used to be that the renderer was vastly improved over standard ZDoom. While this is still true today, the real main draw of GZDoom is that it is now the most updated branch of the ZDoom family, still getting new features today - in fact, there's even another scripting language, ZScript, which is more powerful than previous ZDoom scripting languages were in the past. The result is that even crazier mods are available today, including some that are so crazy that we're not even sure if we can still call them Doom - the engine has been pushed so much that in some cases it only resembles the original Doom engine if you squint. GZDoom can be downloaded here.

Zandronum is unique in that, while it's part of the ZDoom family, it's not a branch in the same way as ZDoom and GZDoom - it's based on ZDoom 2.7.1 (a MUCH older branch of the engine), and in general it operates with one main goal: Client-Server Multiplayer ZDoom. You see, Doom actually had a fairly popular multiplayer scene, back in the day - the only issue is, while most Doom source ports have multiplayer, most of those ports are Peer-2-Peer LAN based. This is essentially fancy talk for "it's a giant pain to setup, a bigger pain to run reliably, and no modern gamer wants to do that." Zandronum is much simpler, in comparison: Download Zandronum and the server browser Doomseeker, search for a server that's active, and simply click join to hop right in. It can be found here.