Work At or ON smth

[XYZ]

Could you please explain me the difference between work AT smth and work ON smth?

And what the difference between these two sentences?

You have to work AT a marriage
You have to work ON a marriage

Thank you.

[bianca]

Some suggestions:

to work at - at home, at the computer, at night

to work on (something, a project and so on) - try to fix something

In your examples, I would say:

You have to work on your marriage (i.e. try to make it work.)