As the runner, can you, when you encounter a server that has Crisium Grid, trash it to make that run successful or do you have to make another run after you trash it?
This is a little technical.
The run is successful, but doesn't count as successful for card effects. This distinction usually doesn't matter.
The point you access cards (and are therefore able to trash) is after the success or otherwise of the run is determined. If you need to make a successful run, e.g. on HQ to trash Off the Grid, then you need to make a second run once you have trashed it.
If you make a run with a card that has mandatory replacement effects on a successful run, e.g. Keyhole, you may access cards (and therefore trash Crisium Grid) since the Keyhole thinks you weren't successful so its replacement effects don't happen.
There's a slightly clunky interaction with Security Testing. The original run does not get you credits because it doesn't count as a successful run for purposes of card effects. However if you make a second successful run after trashing the Crisium Grid, it is not your first successful run of the turn on that server, so you don't get credits there either.
Hope that's clear.