Okay first things first, having read through Ichi the Killer I feel obligated to say - nay warn - you that this series does NOT pull any punches. The imagery used is both graphic and perverse, many of the characters possess varying degrees of sadism/masochism and the implications that are brought up are quite disturbing all in all.
Now with all of this said it's important to note that it is because of these aspects that the story works; because Ichi the Killer does not filter content it can show the darkest part of the criminal underbelly in the least flattering light possible, a light a great many of us prefer not to acknowledge exists. Thus Ichi the Killer is constantly walking a thin line between alienating the audience and drawing them in deeper into the story.
The setting, as mentioned above, takes place in the criminal underbelly (in this case the Japanese red light district) and for the most part has an apartment complex occupied by multiple Yakuza gangs act as the key location. The complex serves a few functions, the most plot relevant one being that it's acts as a cease fire zone for the gangs, which allows for them to live side by side, interact with one another on a "business" level and sort out any problems the gangs may have with one another in a diplomatic manner.
This is where the plot kicks in. We are quickly introduced to four men sneaking into Yakuza holy ground who provide us with some exposition about events that have recently transpired. Through them we learn that their leader (simply referred to as Ji-Ji) arranged for the head of one such gang to be killed by the titular Ichi and that they are going up to clean up the crime scene before the other Yakuza learn of his death, and take whatever money there is in the groups vault. This of course sets off a chain reaction which brings in the underling of the deceased Yakuza boss, the sadomasochistic maniac Kakihara to discover the nature of his boss' disappearance, whilst punishing anyone who may be involved in a gruesome manner.
The story itself follows on the perspectives of Ichi, Kakihara, Ji-Ji and their respective associates throughout the story, giving you their perspectives of the events that have transpired so far. This allows the reader to have a certain level of familiarity with the plot, though it also purposefully withholds certain details to maintain a level of tension to balance this out. By the end of the series there are some unexplained points that could really use proper explanation and certain elements when the focus is squarely on Ichi do drag down plot progression early on, but neither of these stop the end of the series from having a certain kind of payoff.
The characters in general feel fleshed out (if a bit focused on a particular character trait) and play off each other well. As this is the kind of series where people are killed in particularly brutal ways characters will often get a bit of character development before they meet their maker, which helps them leave an impact on the reader even if they might not have particularly cared for the character that has just died.
A lot of the enjoyment from Ichi the Killer stems from the humour, which ranges from pitch black to comparatively light hearted, this helps balance out the pure sadism that is frequently displayed by several characters. It should be noted that if you're particularly sadistic yourself that you may get a kick from the over the top-ness of some of the violent scenes presented, though this becomes much harder to do as the scenes get increasingly bloodthirsty.
Finally, as the artwork is of particular mention, it has to be said that Ichi the Killer is superbly drawn. Both characters and background environments are consistently drawn on model and in high detail, with each character looking distinct enough that you'd be hard pressed mistaking a character from this Manga with a character from another one. Fittingly this also means that the torture scenes (all of which are downright sickening to think about) never miss a beat either so be sure to keep that in mind.
So if you're looking for a unique psychological Manga and can stomach themes of sadism/masochism, full frontal nudity, grotesque torture and violence that goes into overkill territory then I recommend giving this a read, though if you ever begin to get squeamish during or just by reading about it then give it a miss, if anything that's the sensible thing to do.