There are various cuts for emeralds, with the best cut being one that you like. The historical cut for emeralds is the namesake emerald cut, with the asscher and octagon cuts created with the same techniques. Other cuts like cushion and oval are not necessarily less popular, but more unknown as cuts for emeralds.
E1151 | “Emerald ID: E1151”
E1423 | “Emerald ID: E1423”
E167 | “Emerald ID: E167”
E1349 | “Emerald ID: E1349”
E1556 | “Emerald ID: E1556”
E1514 | “Emerald ID: E1514”
The emerald cut was designed to be gentle on emeralds since they are relatively brittle, with asscher and octagon cuts using the same techniques. Once set in a ring however, your finger will break from being hit before the emerald does. Not to mention this cut was developed over 500 years ago, with better faceting techniques, knowledge, and equipment for cutting gemstones of all different shapes being available now.
A relatively new cutting development is cutting gems using a laser. The laser actually burns away parts of the gems, but it allows for the “cutter” to create cuts that are impossible to execute otherwise. This is usually done on more common gems that grow to large size.
A famous example of a fancy, also termed fantasy, cut is the Dom Pedro Aquamarine. I selected the aquamarine because its mineral species is beryl, same as emeralds. Unlike emeralds they grow to huge sizes like a person’s forearm, and usually form inclusion-free. This makes them popular for the fantasy cuts. The Dom Pedro is the largest cut, gem-quality aquamarine in the world, though it was not cut using a laser according to public knowledge. Whatever the exact techniques used were, the sculptor does not disclose his carefully developed secrets.
The emerald cut is the historic choice, demanded by practicality of the emerald breaking otherwise. With all of today’s tools and technology however, the best cut is your favorite cut. In order to get the really crazy cuts, you will need to contact a specialist.