The national criminal history database is maintained by the NCIC (national crime information center). When a criminal history check is done, The charge, the ORI of the charging agency and the outcome of the charge is reflected. In most cases, Guilty, not guilty, dismissed (prosecutor dropped the charge) or Nolo contendere aka I do not wish to contend (fight) the charge, shows up as the result.
In a general criminal history check, the ones that 95% of employers, outside of the aviation world have access to will not show anything if your results are dismissed or not guilty. Nolo contendere, because it is basically the court or prosecutor offering you a plea deal and Guilty will show up on a basic criminal history check.
An arrest does not guarantee a criminal history, the local prosecutor must "file" charges in order for one to have a "criminal history". If for instance, you are arrested and the prosecutor does not go through with filing charges, you will not have a criminal history.
In most jurisdictions to expunge a criminal history charge, one must have been found not guilty or the charge must have been dismissed. To do this, you need an attorney to "petition" the court as to why the charge should be removed from your criminal history. If this is granted, the court will contact the NCIC center and the arrest/charge can be permanently removed from your criminal history.