I've been meaning to read this collection for a couple of years, ever since hearing 'Understand' read on BBC Radio 4, and my only regret is that it has taken me so long to get around to it. To follow are reviews of the highlights, although all the stories were excellent. 
 From the first story, 'Tower of Babylon', I knew I was in for a rare treat. This is simply superb science fiction - told from the point of view of the science and technology of the time. It imagines an impossibly tall tower built of kiln-fired bricks (as sun-dried bricks would, of course, not be strong enough) to reach up to the vault of heaven and thence cut through it to reach Yahweh. Chiang describes the denudation of the land around Babylon as it has been stripped of timber and the chasm around the river from which clay has been mined for bricks, and the wooden platforms high up the spiraling ramp on which vegetables are grown by those who live part way up the tower - necessary as the trek is of several months duration to climb the immense height. He describes passing the orbit of the moon and seeing its pocked face hurtle by, and the immense heat as the orbit of the sun is passed, and the precautions taken against releasing a second deluge by inadvertently broaching one of the great reservoirs that the vault is surmised to contain. 
 From the view of the science and cosmology of the time, all this is reasonable and logical. Indeed, it treats the technology very much like SF from the early 20th century did (and probably still does) positing the most extremely favourable outcomes beyond the limits of what is actually achievable, in order to tell a good story and reflect back upon the ideas of the society. Just wonderful. 
 'Understand' is the tale of a man who, following the repair of brain damage by a new drug, realises that his intellect is growing at an exponential rate. Very reminiscent of Flowers for Algernon, of course, a very well written classic SF story that deals both with how he deals with the changes but also touches upon the fact that his way is not the only approach. 
 'Story of Your Life' was probably my favourite. A linguist is called in to help communicate with aliens who have dropped communication devices around the world. Chiang addresses some of the classic SF ideas of alien contact - will we be able to use maths or physics as a common language? will our perceptions simply be too alien to each other to allow meaningful conversation? - and intersperses this with personal memories of the narrator. At first this seems to be purely character building for it's own sake, to give background and context and depth to the character, but about halfway through you realise that the difference in outlooks between the two species, human and extraterrestrial - and therefore how their languages are constructed - which is the thing that is confounding communication, can be bridged, and in doing so this alters the communicators. The story becomes an exploration of how language shapes our perceptions, but also upon humanity and time and loss. It left me in tears. 
 '72 Letters' is similar to 'Babylon' in that it takes a set of pre-enlightenment 'scientific' ideas and runs with them. In Victorian Britain, progress is based on manipulation of Kaballistic language and the constructs they can be used to animate. Again, a wonderful meshing of ideas with a superb internal consistency, used to propel a gripping tale. I would quite like to see this expanded further. 
 'Hell Is The Absence of God' posits a world that has proof the Judeo-Christian god exists because his angels regularly make appearances - events which can enact miraculous cures but whose violence usually also results in death and destruction - and because there is evidence of Heaven and Hell - the latter being much like mortal existence except the Hellbound are eternal removed from god, but occasionally visible in their existence. What makes the story brilliant is that it takes a set of rules - god exists, heaven can be reached through unconditional acceptance and love of him, his plan is ineffable - and shows a world that is, in effect, no less confusing and random than the godless world that we inhabit. Chiang intertwines the tales of several people in various levels of acceptance (the word 'belief' hardly seems appropriate) - including a man whose wife is killed during an angelic visitation and a woman who is is born deformed but begins to lose her faith after being healed - that show the human condition does not easily resolve to simplistic answers, no matter how much we may want it to. 
 The closing story, 'Liking What You See: A Documentary' is as clever as any of the other stories, but explores more deeply, perhaps, than 'Division By Zero' or 'The Evolution of Human Science'. Taking the form of clips and talking heads in a documentary, it explores the impact of a nascent medical technology that, when implemented, blinds the subject to the physical attractiveness of other people. Part of the focus is students at a school where children have had this done from infancy and much of the rest conflict between opposing sides of a culture war, one of which sees this as part of the ongoing movement toward equality and the other as warranted interference, along with non-aligned voices from elsewhere on the spectrum of opinion, and beyond. As well as exploring the "halo effect" (the tendency when you see someone who is attractive to assign to them other favourable characteristics such as intelligence, strength and moral rectitude - and if you don't think you do this, trust me, you do - Chiang also looks at how commercial advertising interests react as well as the more subtle and less concrete ways in which appearance - others and our own - matter to us. What in lesser hands could be an interesting but glib story of a single idea becomes a wonderful thoughtful gem which, like almost all the stories in this collection, will stay with me for a long time to come.