What is the relevance of a criminal record to employment?

It is not unlawful for an employer to deal unfairly with an employee because he or she has a criminal record. This applies to a decision whether or not to offer employment to an employee with a criminal record. There are many employment positions where a particular criminal conviction may render the employee unsuitable for particular employment, for example illicit drug consumption by a prospective pilot or sexual misconduct with children in the case of a teacher. That is self evident.
However, it does not follow that a person with a minor convcition for dishonesty cannot make a career as a bank officer, and a person with even an appalling driving history in his or her youth would not mean that the person would not make an outstanding police officer.
The Fair Work Act does not prohibit discrimination on the grounds of a criminal record, although it is unlawful to do so in Tasmania and the Northern Territory.
The Humans Rights and Equal Opportunity Commission (HEROC) is a federal body and it is empowered to conduct compulsory conciliation where a complaint of discrimination on the ground of a criminal record is made to it. However it cannot arbitrate a dispute and is therefore a toothless tiger.
Having said all of this, the point should be made though that the dismissal of an employee based on his or her having sustained a criminal conviction may well be held to be an unfair dismissal.
Curiously perhaps it is not unlawful to take adverse action against an employee for a criminal convicition because that is not a prohibited ground by the Fair Work Act.