"Tower of Babylon" is set in a Mesopotamia where there really is a vault of heaven for a tower to reach. In "Understand" an experimental drug makes the protagonist really, really intelligent, capable of understanding not only the world but his own mind. And "Division by Zero" is about a mathematician who discovers that arithmetic is inconsistent.
In "Story of Your Life" a linguist is drafted to help decipher the language of heptapod aliens. Interspersed with the narrative of her linguistic discoveries are vignettes of her lifetime relationship with her daughter. At first these two strands appear to have no connection at all — and their link turns out to be indirect, involving variational approaches to physics and a different kind of consciousness, challenging our notions of memory and free will.
"Seventy-Two Letters" is set in a 19th century England where industrialisation is kabbalah-inspired, with automata (golems) manufactured by applying names to sculptures. And reproduction works in accordance with preformationist theory, with tiny homunculi recursively nested inside sperm. This is mixed up with some politics, involving eugenics and class tensions, and some action.
"The Evolution of Human Science", originally published in Nature, is less a story than an abstract speculation about how human science might react to a "metahuman" population with a superior but incommunicable knowledge system.
In "Hell is the Absence of God" angels regularly visit the earth, dealing out miracles (and incidental damage); statistics are kept on the results, and on the fraction of people who are taken to Heaven or condemned to life in Hell, without God. The lead character is desperate to learn how to love God so he can rejoin his dead wife in Heaven; two other characters face rather different challenges.
Presented in a documentary format, with short perspectives from different people, "Liking What You See" is set in a near future where it's possible to reversibly modify people's brains so that they don't perceive beauty or ugliness in faces. A progressive university is debating whether this, known as calliagnosia, should be a requirement for students.
The significant novelties involved in Chiang's stories require some serious suspension of disbelief, but he manages this well. He doesn't dwell on the presuppositions or back-story, attempting to justify the impossible, but rapidly introduces the setting and elaborates on it only as much as is necessary for the plot and the exploration of ideas. (The occasional exceptions are jarring, for example in "Story of Your Life" when some nonsensical argument is presented to explain why the aliens haven't learned anything from human television broadcasts.)
None of the characters have much depth. They are driven by intellect rather than emotion and their personalities presented from the outside, fairly clinically. A focus on their understanding of the world is arguably necessary for the elaboration of the story ideas, however, and there's only so much that can be fitted into a short story. (I am not convinced that Chiang could produce a decent novel using the same approach.)
The plots work effectively, both in unfolding the implications of the central ideas and in holding the reader's attention. This is true both in the stories with straightforward chronological narratives and in the more unusually structured ones, with resolutions provided by a mix of goal seeking, problem solution, and structural cadence.
Stories of Your Life and Others is the most entertaining and thought-provoking collection of science fiction stories I've read for a long time.