Random Campaign

A series of linked wargames where the next game/scenario is randomly-determined. Notably used by Games Workshop in many of their skirmish games. Popular with smaller groups, ones without a GM, and players who don't want to burn time setting up the campaign. Setting up, tracking progress, and scheduling future games in the campaign are all very low-overhead. Compare to Map and Ladder campaigns

Mechanics

There's a limited table of scenarios. Players roll to see which one to play next. It's usually a weighted distribution, with some scenarios being much more common than others. Players, especially the lower-ranking player, may be able to adjust the dice roll or use special abilities to force a specific one to come up next. Certain Injury results (like Captured soldiers) may also bypass the roll when the game is tracking individual troopers. Narrative is mostly what the OSR calls "emergent". Which is to say you make most of it yourself based on all the random crap that the tables make happen to your dudes. There's very little narrative tying any one game to another, besides the forces involved and the players' desire to make it so.

Random campaigns technically work at all levels of play, but mostly show up in skirmish-level games. Since there's so little meat to the way you select each game, it frees up a lot of space for players to track individual characters in their force. Most of your unit variations, limitations, and advantages come from what you can afford to bring to the next one. These games will often have involved post-game sequences that are also heavy on the random tables.

As the GM, you will only need to set up the tables for rolling up each successive game. Source a few scenarios and go. Each of your players will quickly grow to prefer different scenarios, and making complex/unpleasant ones show up commonly can drive people away very quickly. On the other hand, since the dice are choosing games (rather than the players) it tends to bust people out of ruts where they only play the simplest games. It also means that players are most-likely going to blame the dice rather than you if they get shafted.

Variants

Pretty much every variant is just some way to make the next game in the campaign less-random. The player with the lower Gang Rating/available PV might choose the scenario from a list of available ones for each dice roll, or be able to add/subtract a point from the number originally rolled to get closer to the one they want. The GM might also interrupt the random games with set-piece scenarios, like a King of the Hill match, or place clues as objectives in one week's scenario that unlock new games or random tables later. There are also a number of hybrid systems. In Frostgrave and This Is Not A Test, players can interrupt the semi-random campaign structure with one-off scenarios by mutual consent, while in Gaslands' campaign system you can run a random scenario in-between the fixed league games to collect bonus resources.