The Three Body Problem of the first title is the alpha-centauri system: starting from how life might have evolved there, and what it might do when discovering life around its nearest star, us, is how the plot gets going. Three books later, centuries into the future, the horizon was still expanding, the plot was still unfolding and I found myself stunned and captivated by the ending.
The second fun thing about the books is the Chinese provenance, totally fascinating and an unusual bonus in a sf book. As well as some of the settings, I love the way that the Chinese are the real flesh-and-blood characters and the Westerners are on the fringes; just the opposite to Western-inspired fiction.
Having said that, you wouldn't read the books particularly for the characters, dialogue or relationships. Another thing to mention is they get a little slow at times with Chinese/Communist preoccupations like lengthy discussions about controlling the morale of the people: all irrelevant in the West where no-one controls the public discourse.
Nothing about this spoiled these stories for me, which is the best SF I have read for years. I am a reluctant reader of long trilogies but it was easy to make an exception this time.
I can't think of higher praise than to say Liu Cixin reminded me of Olaf Stapledon, the father of SF by some measures, in his sheer astonishing imaginative breadth. He seemed to think of everything; later writers in the genre merely filled it out. Liu Cixin has a brilliance of the same kind.