The leader in this regard, GIA is a non-profit involved in research into jewelry and gems, as well as education on the same. All kinds of gemstones are studies and graded here. Their trained gemologists also serve as a source of research support to the diamond industry.
Based in Antwerp and owned by AWDC, HRD uses similar standards to GIA and is very reliable in their grading.
This is an organization membered by suppliers, jewelers, traders, and appraisers. Since 1966, AGSL has been using their own set of standards when it comes to grading diamonds.
IGI, GSI, and EGL
IGI has labs in several countries, as well as a gemology school. GSI too is well spread around the globe. EGL is the least credible of the diamond grading labs.