Software wiping
Overwrites every sector of a working drive so data can't be recovered, while keeping the drive usable. It preserves the most resale value and is well suited to equipment that will be remarketed.
Degaussing
Uses a powerful magnetic field to erase traditional hard drives and tapes. The media is no longer usable afterwards. It does not work on solid-state drives.
Physical destruction
Shredding or crushing drives makes recovery impossible and is often required for highly sensitive data. Destroyed drives are recycled for their materials.
Always get documentation
Whatever the method, ask for a Certificate of Data Destruction listing serial numbers, so you have proof for auditors and regulators.