There is no single answer to this, unfortunately, as dueling was an institution found in a number of countries where it was conducted in different ways, and declined for different reasons. For instance while dueling ended in the UK by the mid-1800s, Uruguay saw its last duel only in the 1970s, and only recriminalized the practice in 1992 (the law allowed for duels to be a misdemeanor if following certain practices). I've written about the decline in various places and times, so would direct you here for Canada and here for the UK. This discusses Russia, while I look at the tail end in Italy here and here, with the second one also looking at Germany in the 20th century.

If there are any follow ups, or specifics your interested in, I'm happy to expand best that I can.