In the UK, employers can check original documents in the candidate's presence, use the Home Office online service with a share code, or, for British and Irish citizens with a valid passport, use a certified digital identity provider. A copy of the check is generally kept for the length of employment plus two years. People with time-limited permission need a follow-up check before it expires. Other countries have their own processes, such as Form I-9 in the US.
A correct check protects the employer from civil penalties for illegal working, and the rules change, so current Home Office guidance is the reference point rather than habit. To avoid discrimination, the same check should apply to every candidate at the same stage, not only to people who appear to be from abroad. This summary is general information about UK practice, not legal advice.