Raising kids in a technological world

Do any of you fear for your children's safety with the technology we have today? I am a big fan of technology but not so much social media. It's one of the things I worry most about raising my daughter. For those of you with older children, how do you keep them safe while on the computer? If your children have a Facebook or something, do you ask for the password so you have access to their account? Where to draw the line between safety and giving them privacy?