Finished reading these books recently and thought I'd write a short review since I don't see the series talked about much here in the same way as other popular books get mentioned. I have avoided any spoilers to events that occur.
The series, 4 long books, tell the story of the political, military, and technological history of the island of Dara. The setting is fantastic with soft magic that does not get explained, and is not very powerful (think Lord of the Rings where the Elven rings or Gandalf's magic). At the same time, the island has developed a steam-punk sort of technology that allows them to develop things like dirigibles with lighter-than-air gas. The setting is inspired by Chinese culture, and I think those with more (read: and) knowledge of Chinese history than me can explain further which dynasty and families it takes inspiration from.
The series is split up into two parts I would say. The first part, which is the first book, is concerned with the creation of the eponymous Dandelion Dynasty, while the following three books re concerned with how the events of the first book affect Dara. Because of this, the first book offers a natural stopping point before the final three (which is what I did, waiting a almost a year to start and finish the last three books).
What this series does very well I think is the portrayal of clearly flawed characters, whose flaws actually affect their lives in lasting ways. It isn't so much that their flaws are plot devices that they must grow past to succeed, but that in many cases they cannot escape their personality flaws for better or worse. Does this mean that the characters don't change? Growth isn't a given, which I found to be very realistic, since sometimes character flaws are themselves presented as narrative drivers that only really exist to drive the plot forward (e.g. there are no arrogant characters whose main job is to grow into a humble character).
When characters do change, I thought that they changed in a way that was expected based on their lived experiences, even if it takes a little while to fully understand how or why those experiences have manifested in the ways that they ended up manifesting.
Structurally too I think Liu does a very good job at arranging the story. It is for the most part told chronologically, except that often times there are inserted analepseis that fill in why things are the way that they are. For example, one thing he is very fond of doing is describing a battle over several chapters, inserting between each "part" a flashback to explain how a particular military invention or tactic came about.
Speaking of martial matters, I thought (from someone who doesn't read much military fantasy) that he did a very good job throughout the series describing the battles and the unique tactics that got used during each, which made the battles actually interesting to follow along with.
Tonally, the series has a fair bit of the sentimentality you'd expect from Liu if you're read some of his stories from The Paper Menagerie. It can be a bit sappy some of the time, but he balances this well with a good mix of positive and negative emotion. It has heartfelt and sweet moments and emotionally devastating moments.
The pacing of the series is, I think, very well done as well. For something like 3700 pages over only four novels, each novel avoids the pitfalls of writing a slog of text that only resolves at the end. Each novel has several high points so things build up and release several times. Things that occurred previously are also intentionally written. A fan of Chekhov's gun, most all (as far as I can tell and remember without being overly meticulous) things that happened seem to get mentioned for a point later on.
The world building is pretty good, too (although I don't know how much is simply directly lifted from Chinese philosophy; I do no that he does overtly lift from ancient Greek literature quite a few times, though). The world certainly feels lived in and that it has a distinct history. And he makes good use of "historical" (for the world) allusions and references to previously written texts, artwork, leaders, generals, etc.
One of the weaknesses of the series is the writing. At times it can be quite good. The beginning the first book struck me, but it feels as though the more Liu wrote the more he became more lax with his writing. At times it can be a bit cringe-worthy. At several points in the final book he writes stuff like "She found his attempt to out-Lyucu the Lyucu almost laughable." I think the writing is good, but I wouldn't call it excellent. Typically I am a snob when it comes to prose style, but I think the other elements of the novels are compelling enough to accept some occasionally cringe writing.
One other thing is the use of conceptual metaphors that have no place in the world. Consider this:
"By using the ice as a kind of cement, the defenders could build the wall far higher than the traditional method of packed snow and loose logs, adding even more strength to the fortress."
Except, the world has no cement. So this simile, and the frequent use of the metaphor of "cementing" things are starkly out of place. Does this matter? For writing purposes, it does for me since I couldn't stop thinking about it once I noticed it. But for the vast majority of people, probably not (and it certainly doesn't affect the story itself).
Ultimately this series was excellent. Its up there with my favourite fantasy and sci fi series, only knocked down from being incredible by the varied writing quality. Would (and do) recommend this to anyone who enjoys epic fantasy.