The Cut of a diamond is the biggest factor in how beautiful a diamond will be... meaning that if a diamond is cut to exacting angles and proportions, this jewelry potential beauty will be realized. The other big change has been the wide spread use of diamond grading reports, which have become a "must have" part of the transaction. Even with these changes in this buying process, a diamond's Cut can still be a minefield of misinformation and confusion. Just because a diamond has a grading report it does not guarantee that will be beautiful.
When considering a diamond that comes with a grading report, it is best if you only accept grading reports that come from GIA, AGSL, or GCAL. These jewelry grading reports do have a Cut grade that can be trusted and that can be used to compare with others.
Just imagine the process everyone should go through when considering buying some diamond jewelry from a local jewelry store. I am amazed by the amount of incorrect information about diamonds that exists on the Internet. In the search for the right diamond or piece of jewelry it is always best not to be distracted by the siren's song of low prices. Your local retail diamond jewelry store might have higher diamond prices (maybe they might be able to match online diamond prices!) but they also have diamonds that you can see before you buy.
They might have a good trade up program, they might offer a free appraisal, they might offer free checkups / cleanings, they might offer free ring sizing's, they might offer lifetime damage or loss guarantees, and a this jewelry purchased from them could have the added cachet of being a piece of diamond jewelry from Tiffany verses a piece of jewelry from them site.