Burraco history is a topic that we cannot talk about without mentioning the game of canasta. The reason why this is true is the fact that burraco is a variation of canasta (you can also read about burraco game variations). We are basically in front of the same game but with some differences that do count at the end of the day.
Canasta can be considered a classic card game. It first appeared in Uruguay and then became really popular in Argentina. The turning point in Canasta history (thus burraco history) came with the game reaching Latin America. This is where its popularity rose considerably and then it was only normal that the game would also gain a lot of success in USA around the fifties. 
What is interesting is that canasta was at one point in time the most popular card game that people were playing. At that point in time we saw the development of official rules and thus the appearance of the Classic Canasta game. As time passed people wanted more diversity and this led to appearance of different variations. Burraco is one of the variations that are highly popular in Italy although we now see that many are interested and new players appear every day.
Nowadays we can look towards the history of burraco as one of little interest due to the fact that it is a game variation. The future will probably be different since we are noticing a lot of changes in trends. Canasta is not gaining popularity while burraco is. We expect to see a lot more players that will enjoy this game and will mainly look towards online play.
The good news is that online casinos and rummy rooms have realized that burraco will be a big thing. This is why most establishments have already included the game. There are dozens of sites where you can play for free or for money. We recommend that you look at the bonuses that are offered and then you decide where to join. Just make sure that you always join legit sites that will have a big degree of security and a valid gambling license issued by an authority that you can trust.