This is a preliminary explanation of why this show is so awesome; I promise to do an edit/real review when it's over. (Edit: See below)
As a literary nerd, the game of karuta has long delighted me. If you like poetry, literature, love stories, or Japanese history check this anime out right now! Do it!
If you want to read the poems as the show airs, skip the online wikis. My suggestion is Peter McMillan's highly acclaimed One Hundred Poets, One Poem Each; he's a poet as well as a scholar and does an excellent job with the translation and notes. The book is very readable, and jam-packed with background information, brief poet biographies, calligraphy, interpretations and explanations of multiple layers of meaning, and plain kanji and romanji--so you can watch an episode and then thumb through to reread (and memorize?) the poem. <3 <3 <3
I wrote that last bit when the show was first airing, and, as promised, I am back to edit the review and do it properly now that the show is over.
Story: Generally, each episode was a self-contained story or two, however, as the show progressed, it did a good job of having old characters come back and pop in to say hello. I thought this was a successful approach, because you are reminded of previous characters and are shown how they may have known each other irl.
The only things that irked me about the story was the intrusion of modernity, in two forms. First was the activities Teika did to introduce the show (variety show interview, super hero show), and second was the use of English/katakana words. I may be a little picky on that last one, but for heaven's sake, it was a historical anime and they should have at least tried to use all-native-Japanese words.
On the other hand, I *really* liked the part at the end, where they talked about poetry and human emotion always being relatable, even across a thousand years. That was cool. Also cool was the 12th episode, which amounted to a fabulous, serious feminist critique of society.
Animation: I liked the patterns and the use of lines in clothing and whatnot. I thought the dark, bold outlines around the human beings made them look a little like puppets. Puppets + poetry = theater = very fitting atmosphere for the show.
Characters: Good well fine, but maybe best classified as interpretations of real people based on what they wrote and what was written about them. I loved all the ballsy-yet-classy lady poets, and the depth and complexity of personality attributed to each character that was focused on.
Overall: So that thing I said about human emotions and being able to relate to them no matter the culture, century, place, etc? That is why the Hyakunin Isshu will live on in history. Nothing about the poems is contrived or fake, and the show is worth a watch if you like learning about history through the stories of individuals.