Recently I filmed a 2v2 exercise with a progression leading to a defender chasing from behind of a 2v1. This setup can easily be used for 1v1's-3v3's and most things in between. It can be used as a numbers game adding variation between how many from each side can attack at the time while forcing all players in the line to stay on their toes.
A common flaw with these sort of wave like exercises is that there is no time pressure for the attackers, they are free to stay on the ball knowing all defenders are in front. By adding this progresion however, they must continously scan for space, team mate and opponent knowing this will change very quickly with the defender pressing from behind. The technical skills to controll the ball while running at a high speed is also a skill learned/practiced in this progression.
This is suitable for the second part of warm-up/before going into matches and can be seen as a technical exercise due to the low complexity and tactical specificity. It gives a lot of repetition on match situations while taking away a lot of options decreasing the complexity.
Knowing that only 30% of the 1v1's in the game are frontal (face-face) it makes sense to practice games like this where they receive pressure from varied angles. For more characteristics of 1v1 situations in games see this article.