The basic concept of an All-Kill Format is “winner stays on”.
The All-Kill format is a way a team league or tournament can be played. The difference to the conventional team format is that the complete lineup isn't announced before the match, but only the first player of both teams. These players will face each other on the first map of the map pool. The maps are predefined for all games — the players, except the first ones, are not.
After the game between the first two players, the winner will play again. The loser is replaced by a player, who is chosen instantly after the match to challenge the winner of game one. This goes on, until the victor is determined. Usually the All-Kill format is played as a best of 7. That means the first team achieving 4 victories is the winner of the match.
Perhaps the highest profile instance of this format was the GSTL, nowadays the SPL playoffs.
One variation to the standard All-Kill format is only the first two players and map are announced and the losing team also chooses the next map from the available map pool.
An All-Kill is when one player takes out every other player on the opposing team. Below is a list of the players who have accomplished that feat.
If the opposing team has almost completed an all kill and your last player (or "anchor") is the only one left and s/he then goes on to do an all kill of the opposing team it's called a reverse all-kill.