His tournament record includes the following achievements:
In 1927, Vuković played on second board for the Yugoslav team at the 1st Chess Olympiad in London, posting a record of +7-6=2.
Vuković edited the monthly chess magazine "Šahovski Glasnik." He is the author of "The Art of Attack in Chess" (Oxford-London 1963), which is widely regarded as a masterpiece of chess literature. Other books he wrote include "Razvoj šahovskich ideja" (Zagreb 1928) and "The Chess Sacrifice" (London-New York 1968).