The Taira Clan is an interesting part of Japanese history. I imagine there’s a fair set of Westerners who have heard of them who have done so through a love of Japanese spooks and thus the infamous Taira no Masakado. But, there’s history behind the ghost story, itself both widely reported and significantly mythologized, mostly do do with the eventual conflict between the Taira and their rivals, the Minamoto.
The two clans are also known as the Heike (Taira) and Genji (Minamoto), and their clash, the Genpei War, did a lot of heavy lifting to shape the history of Japan. Though the Minamoto were the ultimate victors, The Tale of Heike is one of the most famed (and period) literary accounts of the war. The Heike Story promises to provide a take on the aged epic.
The main character in the anime here is Biwa (so called after the instrument she loves), a heterochromic girl orphaned by the Taira who has some ability of future sight. Naturally, she has little kind to say about her father’s killers.

Biwa makes her proclamation to Taira no Shigemori, the acting lead of the clan and a fair and level-headed individual. Not only is he innocent of the abuses of his kin, he also has his own magic eye, with which he can see the dead. This strange connection leads him to take Biwa in and make her a playmate for his children.
Thus, we see the waning years of the Taira clan through Biwa’s eyes, how Shigemori tries to steer them to a just route while his father and the leader emeritus Taira no Kiyomori acts the part of an old troll and fans the flames of conflict over his petty desires.
A while in, the conflicted, skilled, and diplomatic Shigemori dies. Biwa inherits his spirit sight, but more critically this puts Kiyomori back in the spotlight. While volatile, the old man is ambitious and skilled, and shortly enacts a coup. He replaces many dignitaries with Taira stooges, eliminates rivals, kidnaps the old emperor, and installs his infant grandson (admittedly a proper successor) on the throne. He even moves the capital from what we would know as Kyoto to Fukuhara, his personal port city.
This inflames sentiments against the Heike, resulting in the Genji, their long-term rivals, being called to resist Kiyomori’s domination. Though in halting steps, what we would know as the Genpei War begins. Even as the capital returns to Kyoto, the violence only seems to intensify, drawing in more of Japan, mostly against the Heike.

Kiyomori himself passes not long after the return to Kyoto, but all this seems to do is leave the reins of the Taira clan in less competent hands, including one of Shigemori’s sons finally kicking Biwa to the curb.
Thus, we enter a new phase. The star of the Taira falls, sending them running with their tails between their legs, the presumptive child emperor their last claim to power. Biwa, meanwhile, seeks her mother, eventually finding the old woman and coming to understand her purpose. As the Heike meet their ends, one by one, she returns to witness the final battle at Dan no Ura. There, as per history, the Heike are wiped out. The only survivor among them is the mother of the young emperor (himself taken into a suicide by his grandmother), who goes on to become a nun while Biwa composes the epic of the once mighty clan’s fall.
Thus ends The Heike Story
The summary here was short, but that’s because most of the interest in The Heike Story is something of a political soap opera. The next cogent level of detail would have been a play by play bombarding you all with names and incidents. Biwa is mostly an observer to this whole situation, a witness rather than a player in the downfall of the Taira clan. Sometimes, she even takes on a new form to present as the narrator, singing the downfall as it arrives.

Her half-real status is also probably why she never ages, even as years pass.
And, besides her… the tale is about what you would expect from the pitch, a tragedy of politics and violence, small mistakes cascading into inevitable ruin. There are no real heroes or villains. Kiyomori and the old Emperor, for all their scheming, aren’t evil the way we expect of fictional antagonists. Nor are the younger generations of the Taira or the Genji who cast them down heroes in any conventional sense.
The theme of the story, as it begins and ends, is impermanence. The things that happen simply happen. All glories end. Any clan would eventually fall. History would have much the same reminder. Yoshitsune, who led the Genji at Dan no Ura and basically served as the cool and elegant unbeatable boss, would be hounded to death by his own brother’s orders less than five years after Dan no Ura. If you want a compelling Game of Thrones style narrative, just look at the past.
Now, shocking though this may be, I haven’t read the original Heike Monogatari, even in translation, so I can’t speak to how well The Heike Story captures its subject matter. But what I can say is that it absolutely evokes a certain mood. It conveys a deep futility of victory, yet tragedy of defeat. To its characters in particular, it creates an odd sort of attachment. The deaths of the various sympathetic Taira are tragic, but something in the mythic presentation numbs the pain. It’s sad often, but never shocking.
To that end, what The Heike Story probably does best is present as mythic fiction. Even the art style evokes a sense of age and weight. What’s more, it does this organically. Too many productions, in Anime or in Western media, are desperate to feel big and important, not realizing that striving for it ironically tends to disqualify a piece on some level. The Heike Story, naturally, has source material perfectly fitted to the sentiment, but it still had to stick the landing on its own.
This is a weird one. The grade I’ll give is an A, and I was honestly debating bumping that up, but… this is more for artistic accomplishment and expression. I wouldn’t recommend The Heike Story to a casual viewer lightly. It’s something that deserves to be, needs to be chewed on with some effort in order to properly digest it, making it a watch unlike most anime. Take from that what you will.