Although the conspiracy theorists won't buy it, I think it's worthwhile to give an outline of the actual history of the Rothschilds.
There is no such thing as the Illuminati. There used to be a group in late 18th century Bavarian called the Illuminati. They were shut down by the government and ceased to exist.
Most conspiracy theorists possess a very poor understanding of history and a disinclination to read actual history books, and thus they miss out on finding out how history is actually really interesting without having to embellish it with conspiracy nonsense (though admittedly, many conspiracy theorists have mental problems that lead them to these delusional beliefs).
There's no doubt the Rothschild family (who are distant cousins of mine, though it's fair to say that anyone who is descended from early 19th century Anglo-Jewry are probably distant cousins) were extraordinarily powerful in the 19th century. The story about buying up all the consols after the Battle of Waterloo is true. There were also other families like Baring who were very powerful ("The shares are a penny and ever so many are taken by Rothschild and Baring", if you know your Gilbert and Sullivan).
They (families like Rothschilds, Baring, Coutts, etc) were essentially the central bank of their day, and the fact they had large holdings in railways made them tremendously influential. However, they started to falter by the 1920s. The Rothschilds great advantage had always been that they were a pan-European banking family, and that they had something akin to an intelligence network and couriers who would take information between London, Paris, Vienna, Frankfurt etc to give them tips so they could lead the market before the information became general knowledge.
Things were already challenging at the beginning of the 20th century, as mass media and communications like telegraphs, newspapers, radio (from the 1910s) proliferated, their inbuilt advantage in possessing information in a time of slow communications started to fade. Also, in the first few decades of the 20th century, the partnership structure of their business (owned by family members as partners) began to be a hindrance; they were going up against competitors which were publicly limited companies that raised capital through the issuance of stock. From the time of the Liberal government of the 1900s/1910s and increasing all the way to the time of Attlee, death duties / inheritance tax decimated their wealth. Whereas as a bank structured as public limited company would never face their core assets being subject to death duties (because the company is a legal person in itself which never dies), the Rothschilds partners faced a swingeing tax each time a generation died off.
The 1940s were a very bad time as both the German/Austrian and French banking houses had their assets seized by the Nazis. While the French banking house got most of theirs back, the German/Austrian house got pennies on the pound. The Rothschilds never really recovered from that. The final death blow came in 1981, when the French socialist President Miterrand nationalised the French banking house, Rothschild Freres.
By the early 1990s, the English branch of the family had a fortune measured in the single digit billions (iirc it was about 3 billion in 1992). They have had a rebound in the last couple of decades, enjoying very strong asset growth and I think Sir Evelyn de Rothschild is worth about 20 billion now. But that is obviously far from the trillions the conspiracists claim
The true history and story of the family doesn't have all the "sexy" embellishments, but frankly I find it far more interesting