How do you remove rust stains?

Hi does anyone have any effective methods they know of for removing rust stains from ceramic and also from clothes? I've tried bleach and it ownly lifts the stain slightly. My shower floor is covered in rust stains from an old soap container that went rusty. The brown rusty brown speckles look pretty unsightly.

Also I have a white towl that picked up a rust stain somehow and it looks like a big skid mark!

All suggestions welcome

ok thanks guys. I'll look into Barkeeper's Friend and also try some lemon juice on the towel. The stain's been there for quite some time so it's by no means fresh. Anyway thanks for the feedback!