This review does not contain spoilers

The beginning of Yesterday wo Utatte is not actually the beginning. No, but really! It isn't! It may be the beginning for the reader who now starts to follow along the characters' lives, sure, but for those characters themselves, their stories have already been going on for a much longer time! If they actually existed, that is. Though it feels like they do, and it's exactly the achievement of pulling out something like that with enough authenticity that makes Yesterday wo Utatte so great. Instead of only popping into existence once the readers start to observe them, all characters have their own past history, and they show that to a fault in what is a drama about lingering feelings, missed timing and a yesterday that has not been sang.
Initially, Yesterday wo Utatte may feel a bit rough because its actual matter has not been presented yet, though once it gets going, it becomes an extremely engaging human drama that deals with relationships in a way very unique to itself. Without giving any character introductions because that'd be boring or summarizing plot points, I can say that the main plot revolves around a group of characters and their ever tangled threads of love between one another. It's a love net that will perdure through to the end of the manga, and it's from there that the major developments and growths will come from. As mentioned earlier, the factor that makes this different from just any other "run-of-the-mill love triangle, square, pentagon, or whatever it is" anime is that these characters have that authenticity I've mentioned up there. I don't mean that they have a sad backstory. It is not that. What happens here is that there's a statement put to proof: Our pasts build who we are. Yesterday wo Utatte is about the characters' pasts not being about their backstories, but being about the past that still lives on inside them in the form of lingering feelings.
After all, isn't it true that whoever you cross down the street has as much of a lifetime's worth of experiences as you do? Really, isn't it egotistical and self-centered not to think so? A thing that happens a lot with romance media (not stating any kind of qualitative value here) is that when characters meet, they just happen to be either at the perfect time to fully devote themselves for the partner who they just met or they're a blank sheet of paper whose live up until this point, which is literally the very thing that made them who they are, isn't of much interest. Yesterday wo Utatte said no to that. More than about how it shows the characters' lives and connections up until this point, it's about how you can clearly see how important and defining those experiences and feelings are for these characters. Their actions and behavior are a direct result of the live they've lived through up to this point, and here's where this manga really shines.
The majority of these characters suffer from a cruel case, fortunately not fatal, of lingering feelings. Those feelings then become the main fuel for their current actions and decisions because, at the end of the day, it is not easy to let go. From an outsider perspective, it is extremely easy to look at their actions and judge them through rational lenses: "Why do they still feel this way about a fruitless love? They should just give up. Why are they insisting on trying? It's stupid!". Even when you're given full details of what happened that got them to nurture the feelings they have, the same can still be said! One could say that it's stupid to fall in love with a test taker who dropped his school card on the line to the bus and hurried back to get it and you just happened to see that happening, it's arguably a meaningless episode. Then that same one could say that they understand the love born from a life-long friendship that went through their college days and blooms once again upon their coincidental meeting now in adult life. What's funny is that there'll also be people who, upon being given the additional information that the character from the second example has already been rejected now in adult life but still holds feelings for their friend, would now judge lingering on to those feelings as stupid and nonsensical. So where's the line? What's enough of a setback to justify throwing away one's feelings, and what's enough of a connection to validate its blooming? Be it the long-term friendship or the one-time passerby, the only ones that know how meaningful those experiences are are the characters themselves, and that's what I'm trying to get to here. Things in life hold the weight we give them, and that's hardly a rational process.
This leads to what I want to end on and what I think is the best thing about Yesterday wo Utatte: I can't find in myself to blame none of the characters for any of the decisions they take. And this is impressive when you know how much of a turbulent drama this is. There 's no better word to describe it. There's a lot of very serious developments and twists along the way and what the characters make of them are the most dramatic things possible all in order to try and cut the roots of their remaining feelings or to keep those same on life support, no matter how painful either of those are. Many such things look outrageous to the eye of the oh so rational reader, but the empathy needed to step back and properly examine the sentimental reasoning behind the characters' each and every action makes this manga go from a somewhat frustrating adult romance to a masterpiece of human drama: It makes as much twists and turns as any real relationship would, it has characters as indecisive as any real person would be, it shows how sometimes the timing just isn't right and how whether those fruitless feelings are better left forgotten or they still have a slimmer of hope is a duality that has in no way a definite universal answer.
So, to sum it up, Yesterday wo Utatte is a boy meets girl that does not start upon the meeting. It comes from way before that. It's a human drama that excels at what I would like to call "sentimental realism", in which the characters feelings are taken seriously and giving proper value to a fault, not caring for writing rational or gratifying developments, though honestly I'll say that it's exactly because of that bumpy road that the final conclusion is one of the most gratifying and rewarding things I've read, but I'm getting ahead of myself. Each character is worth their own lifetime, and they all make sure to try and show you how they're as much of a person as any other involved in this overcomplicated web of romantic relationships. All of this while keeping a down to earth treatment that does not romanticize the ugly nor deny the beauty of simply giving yourself to your feelings. So, if you have the time, open your heart to a very unique romantic drama that also happens to have a girl with a pet crow. She's great. The crow is great too.