Bans
Moderation > Bans lists bans in force, with a quick check for any Roblox player.
With the Rosterr module in your game, banned players are kicked as they join, with the reason and case number. Adding the module is covered in Tracking activity and quotas.
If Rosterr can't be reached, banned players are let in rather than everyone being kicked.
Game logs
Moderation > Game logs shows admin commands run in your game over the last 90 days, sent by your game script. Check it when you need to know who ran what, and when.