This collection was begun by a raging asshole... the "main" Bhorgese art collector was the nephew of the pope (pope Paul V) which was an actual papal office: being the favorite nephew of the pope came with an official title and was a HUGE seat of power... and this guy, Cardinal Scipione Borghese, used his power and influence as the official papal nephew to strongarm artists, collectors, and even churches into giving him whatever art he desired.
He'd threaten an artist with death, then to commute the sentence, accept as a bribe EVERYTHING in the artists' studio as payment. Which is how he got his fat paws on most of the Caravaggio in his collection.
Not a bad trick... but not a very nice one.
All the early Caravaggio (including 2 presumed self portraits, among them the famous 'Sick Bacchus') was obtained this way, when the Cardinal levied his papal strength against the early Master/teacher of Caravaggio and took possession of everything in that artists' studio... including the work of his student Caravaggio, who was shit out of luck when he showed up to work one morning to find all his work swiped. Needless to say this Bhorghese guy is not the kind of art collector whose radar you necessarily wanted to be on as an artist... although it worked out pretty well for Gian Lorenzo Bernini.
To his credit, Cardinal Borghese - who is still a dick, I'm not letting him off that easy - spotted the talent-in-the-rough that was a young Bernini and gave him his first string of large, expensive, commissions the result of which are the series of large-than-life statues which you can still see in his home today; 400 years later. These are universally accepted masterpieces of the stone sculpture genre; surpassing even Michelangelo according to some. Bernini isn't an artist we hear much about in the USA but he's arguably left more of a legacy (especially in Rome) than any other Renaissance or Baroque artist; and his genius is universally acknowledged and appreciated in Italy and Europe and has been, uninterrupted, for centuries.
This place is really cool and definitely a top 5 destination for art tourists. Somewhat difficult to walk to from where we stayed in the center of Rome, and always sold out in advance (you have to get tickets weeks beforehand, and the tickets are timed so that each group enters for a maximum of 2 hours); it's definitely a "must see" museum of Rome and is on everyone's Top 10 lists for a very good reason. I'd suggest reading up on your Bernini and Caravaggio before visiting... I wish I had, and could only share "bare bones" knowledge about the paintings in the collection with my wife while we were there. But by the time I went back for a 2nd visit by myself, and then a 3rd with my mother the following year, I was familiar enough with Bernini's biography to grasp the chronology of, and importance of, what we were seeing. Loved this.