I have seen the entire series, so perhaps I can help flesh this out a little.
The four young men in question (Aya Fujimiya, Yohji Kudou, Ken Hidaka, and Omi Tsukiyono) work in a flower shop whose name translates to "A Place Where a Kitty Lives." The name of the shop is ironic considering that all four young assassins have codenames that correspond to cat breeds. Aya (or Ran) is Abyssinian, Yohji is Balinese, Ken is Siberian, and Omi is Bombay.
Each assassin has a weapon of preference. Abyssinian uses a katana, Balinese uses a garotte wire, Siberian uses a clawed gauntlet called 'bagnuks', and Bombay is a user of darts and projectiles. They accept missions from a mysterious man called 'Persia' who uses a liaison by the codename of 'Manx'.
Each one has their own reasons for joining Weiss. Aya is getting revenge on the man who killed his parents and put his sister, Aya, in a coma. Yohji is trying to take down the people who caused the death of his partner, Asuka Murasaki, from his days as a private investigator. Ken is trying to find out who framed him and got him ousted out of the J-League (Japanese soccer association). Omi grew up in Weiss and has repressed memories of being kidnapped as a child and left on his own by his father.
Opposing Weiss is Schwartz, which means 'black', an assassin group that works for the mysterious Esset. They are psychics who are, in so many ways, more powerful then Weiss. They are Brad Crawford who is a precog, also known as Oracle; Schuldig who is a telepath, aka Mastermind; Farfarello who seems to have the power to revive himself, aka The Berserker; and Nagi Nayoe who is a telekinetic, aka Prodigy.
Caught in the middle, but still opposing Weiss, is a female team called Schreient, which means 'Scream' or 'Shriek'. They are Hell, Schoen, Neu, and Tot. In the beginning, these women work for Masafumi Takatori, the insane son of the man who had Aya's family destroyed, Reiji Takatori.
The anime seems to focus mainly on Aya and his quest for revenge, which he attains a little more than halfway through the series. However, it also delves into the past of the other characters and what drives them.
Personally, I enjoyed this anime series immensely. The characters are well thought out and the soundtrack is well done. The subtitled version is, as usual, more true to the original scripts, but the dubbed version has its merits, too.
I could go into more detail, but I don't want to totally spoil the series for anyone.