Can you actually see who viewed your LinkedIn profile, or is it like Facebook where you can't?

Unlike Facebook, LinkedIn genuinely does show who viewed your profile, with limits. Click 'Who's viewed your profile' from your profile. On a free account you see only a handful of recent viewers (sometimes just 'someone in X industry'). LinkedIn Premium unlocks the full list from the last 90 days. The catch cuts both ways: if you switch to Private/anonymous browsing (Settings > Visibility > Profile viewing options) to lurk on others invisibly, LinkedIn then hides who viewed YOU too. You can't have it both ways.

The trade-off is the key bit: go anonymous to lurk on others, and LinkedIn blanks out your own viewer list as the price. Pick one.

Free sees a limited rolling list, Premium shows everyone from the last 90 days. If you're job hunting or selling, that Premium viewer list is genuinely one of the more useful paid features.