Since the 19th century, almost half of the diamond trade is done in Antwerp. Aldo the diamond cutting itself nowadays is done in countries with lower wages, the city of Antwerp is still the center of the diamond trade. There is even a whole district dedicated to it. You can find the shops in that district right next to the central station.
Antwerp also has its own diamond museum. The museum is a real treasure house for diamonds and jewelry going way back to the 16th century. Next to the diamonds themselves, the museum also highlights the reclamation and the different steps taken to finish the diamond as you know it.
You can find the museum at this address: Koningin Astridplein 19-23, Antwerp.