This review contains no major spoilers for A Feast for Crows, but it does outline the basic premise of a few characters' storylines and mention the identity of new point-of-view characters. There are major spoilers for earlier books in the series as well.
The contrast between A Feast for Crows and its immediate predecessor, A Storm of Swords, could scarcely be greater. Narrowly the shortest book in the series (to date) as Storm is narrowly the longest, Feast is about the peace following the war that was so violently and definitively resolved in the earlier book. And, because of unforeseen complications in the structure of the series, Feast only features about half the characters from earlier books. This changed to a limited scope and a less rapid pace has caused many fans to treat the book as a failure, easily the weakest in the series. As I've said, I go against the grain a little by regarding Storm as the weakest. I can now add that I go against the grain that much further, in thinking that A Feast for Crows is, given its inherent limitations, the best installment of A Song of Ice and Fire so far.
One of the problems long-time fans have is the introduction of many new point of view characters, and the relative absence of familiar ones. It's true that 27 of the book's 45 chapters feature new points of view, and an additional 12 feature characters only introduced in the most recent book. Inevitably there's some adjustment to be made to the lack of well-known voices, but I find the new points of view so fascinating that it's well worth the effort.
The most prominent character in the book, old or new, is Cersei, who is, after the deaths of her son Joffrey and her father Tywin, the unquestioned Queen Regent of the Seven Kingdoms. The war seems to be over and her other son Tommen's throne secure, but Cersei is far from relieved. She believes the Tyrells, whose support helped her family end the war, are now scheming against her, and the (incorrect) notion that her dwarf brother Tyrion murdered Joffrey has reawakened older, stranger fears. Cersei has always been unstable, but her insanity reaches new heights in A Feast for Crows, and her reflections on previous events in the series expand the character and make her more dramatically credible without obscuring her cruelty. This unreliable narration substantially heightens the novel's mood, of which more later.
The other major new point of view character is Brienne of Tarth, whose quest to find Sansa Stark is essentially all she has to live for. As readers we know where Sansa is, and therefore can recognize just how hopeless Brienne's search is. This could make her chapters frustrating, but the milieu in which they occur is compelling enough that the seeming irrelevance of the plot becomes a minor annoyance. Like Jaime and Arya's chapters in A Storm of Swords, Brienne's storyline shows us the effect of the war on the riverlands, and like those chapters it's plagued with unexpected, highly coincidental reappearance of familiar secondary characters. But there are striking new characters as well, and the riverlands are now rebuilding in the aftermath of war, so the tragedy is tinged with hope.
In addition to Cersei and Brienne, there are nine chapters featuring six new minor point of view characters, who provide a window into events on the Iron Islands and in Dorne. These chapters have also been controversial, with some complaining that their relevance to the overall story is not, as of this book, particularly clear. That's true enough, but in a transitional novel I can forgive the presence of a few dangling threads, especially when the characters and locations are as rich as in these chapters. The scorched land of Dorne, its gout-ridden, cautious Prince Doran, and the daughters and nieces who urge him to throw himself into the game of thrones, are particular favorites, and the vicious lifestyle and Lovecraftian religion of the Iron Islands are, as ever, darkly compelling.
Imagery of metaphorical crows feeding on carrion is prominent in the book, perhaps excessively so, and the Seven Kingdoms are indeed so exhausted by the recent war that only crows can be truly satisfied. And amongst the tentative efforts at rebuilding are forewarnings of the horror to come, creating an atmosphere of prophecy, magic, mental decay, and encroaching doom. A Feast for Crows may not have the scope and speed of A Storm of Swords, but it more than makes up for that loss with a vividly-evoked portrait of characters and a society perched on the edge of a knife, thinking safety is in reach, but actually about to be skewered.