Gemological laboratories issue reports after scrutinizing a diamond. This certificate analyses everything- cut, clarity, colour, dimensions etc. These reports are reffered to differently by different institutes:
The Gemological Institute of America (GIA) - Diamond Grading Report and Diamond Dossier
American Gem Society Laboratories (AGSL) - Diamond Quality Report or Diamond Quality Document
The European Gemological Laboratory (EGL) - Diamond Certificate
The International Gemological Institute (IGI) - Diamond Report
When you purchase a diamond, the original certificate must come with it. These are needed to insure the diamond.