Along with the regular tournament types such as Random Battle or OU, over time users have created some of their own formats:
Survival Showdown is a tournament where there will be two teams (usually 3 or 4 players on each team) that will battle against each other to see who is superior. Each time, one person will be selected from each of the two teams to represent their teams in a battle of a chosen tier. The loser of each battle will be eliminated. This continues until either one of the two teams is still left standing, or until one player is left on each team, where they must battle each other two determine the “survivor” of the tournament. Keep in mind that a lot of work goes into this, and could possibly take 2-3 hours or even longer. It is recommended to have a co-host to help you manage the other team, which will make the tournament run a little more smoothly as opposed to just you controlling both teams by yourself.
In this format, all Pokemon on a team are required to share a common Egg Group. Anything that is legal on the OU ladder is legal here. The full list of Egg Groups can be found on this page.