What does Special Forces do besides teach?

So I know that Army SF spends a lot of time teaching the armies in other countries but do they also handle things like hostage rescues and going in to capture high level enemies? Because I mainly only see articles about SF teaching but I figured they might just not be publicizing other things because they're meant to go in and out without being seen. Or is it mainly Rangers and Delta that handle those other things while SF mainly teaches other armies? (Everyone's said that Black Hawk Down is fairly realistic and I know those guys were Rangers and Delta...)