The Boss[]
"The Boss" is referred to a few times in the series, but no one seems to notice or know who this Boss is.
SPOILERS UP AHEAD
The Boss is in fact, Rei Ryugazaki, the highest higher-up in the criminal underworld.
The Boss's specialty is murder and death. He has left such an extensive trail of dead behind, his track record is comparable to that of The Reaper from AssClass. His genius IQ aids him in his plots, and he makes no mistakes.
All of this changed, however, when one day he was on a two-man job and his former partner betrayed him by exposing his identity as The Boss to a third party and taking all the cash. Rei was heartbroken and vowed to get him back, so he created a new identity as an academically-gifted high school student and enrolled at Iwatobi High School.
However, due to his very first run-ins with Nagisa, a spy for that third party caught word he was part of the track team. This, along with the chance to commit murder, lead Rei to quit the track team. Rei now lays low with the swim club and is seen with Nagisa a lot, giving him his wisdom in order to prevent his new partner from making the same mistakes he did.