Looking through a few of the reviews, I'm a little surprised Dogs has so much negative feedback. Since I've been reading it for about five years at this point, I'll try my hand at a review to point out a few key things:
First: Dogs is not for everyone. Seriously. It tells its story the way it wants to and doesn't really give two craps about how much you can understand. Madness is a key aspect of the story with the main character suffering from fits of mania from time to time, and much of his dark past is given in glimpses of disturbing things he experiences during those fits. Fortunately, he's the only main character who experiences these, so all the other characters and plots are not as hard to follow at all. Unfortunately, a huge chunk of the story has to do with him and his dark past, so most of what you really need to know to understand the main story has a lot to do with his complicated, mania-inducing past. If you're thrown off by his fits, don't worry, you're supposed to be. But key plot points are often presented in pieces, and it's really the reader's job to put them together because Miwa does not do that for you. And his characters aren't spelling things out for anyone when they've pieced it together themselves, so don't expect to take the lazy route there either.
However, with that said comes the second point.
Second: Dogs is NOT inaccessible. It may jump around a lot, take whatever liberty it pleases with storytelling, and in general do whatever it wants, but anyone who cares even a little to try and understand should be perfectly able to do it. It doesn't spell the plot out for you, but it gives you all the tools to do it yourself. Whether or not a reader has to go back a few chapters before remembering that important plot point depends on the reader. The only reason I think I have to do that is because Dogs is a monthly release, and I'll often forget what was happening in the last chapter by the time a new one is released. Sometimes, I get busy and may not read a chapter for longer than that and that makes it worse. Heck, 80% of the time Miwa's opening an entirely new plot with characters we've never seen before, so it gets even more confusing. But anyone reading the story straight through with each chapter back to back should be totally fine. Even just having a better memory than readers like me will probably make all the difference there.
Point being that anyone just casually strolling through looking for an easy read will miss a lot of important things, hit a chapter that makes no sense, and have a huge What Is Going On moment, but anyone who takes the time and doesn't underestimate the details of this story should be able to understand and even enjoy it. It's got an array of really complex characters with complicated pasts, and it all comes down to it all being connected somehow with everyone figuring out just how. We're given entirely different stories, and it's all about watching every different thread come together to form a really complex, but remarkably tightly-woven storyline. It feels like a lot of planning went into Dogs and Miwa hasn't even revealed the tip of the iceberg yet, so that’s really half the fun.
At the end of the day, Dogs has a lot to offer if you're willing to put in the effort. I mean, I still read it after a rough day as a great way to chill out, so it's not a chore in any way, shape, or form, but if you're looking for brain-mush material, it's definitely not that either. You either rise to meet his manga or fall off to the wayside, but Miwa doesn’t go out of his way to help you. He just does what he does and you either latch onto it or you don’t. I recommend it to anyone who likes a manga that has a little more to offer though because, for those who do latch on, it’s a great read all the way through.