Trello shows a historial log of everything that any user has done since the board's inception. Likewise, if you click on a specific card it shows the history of anything anyone has done related to that card.
Keeping track of every change/addition/deletion that is kept indefinitely must collect a ton of data and also potentially bottleneck on writing to the history trail log (assuming it is written immediately to a data store of sorts). I mean, it isn't like they are storing everything in log files spread across 1000's of servers that they only collect and parse when they need to find something -- they are displaying all of this info all the time.
I know this isn't the only service that provides something like this, but how would you go about architecting such a system?