There's quite a lot of info in this question here
Only talking about whole discs:
There are two problems
Is the data destroyed?
Are people who need to know convinced that the data is destroyed?
No software claims to be able to recover data that has been overwritten just once. No data recovery company claims to be able to recover data that has been over written once. No university or other research exists which claims to have recovered data that has been over-written.
In these questions people usually mention Peter Gutmann. His 35 overwrite method was designed for use with ancient drives; there were a small set of passes for each different drive-controller type and you would only use all 35 passes if you didn't know what controller you had. Modern drives all use the same controller, so you don't need to do that many passes.
tl:dr - A single pass of all 0 with render the data unrecoverable to anyone. And that anyone includes governments with scanning tunneling electron microscopes.
But you can't prove the data has gone. There will always be doubts lingering. So, if you work with sensitive data you should just follow whatever the job specs say. Or, if you need to create the specs, follow some DOD standard (7 passes). Or if you want to be really sure, you can just send the drive for shredding.