As you can see, I ended up really enjoying this book. The first 30% or so dragged a bit, because Matthews had to do quite a bit of backstory in order to set up the second two thirds. The book starts out with the two main characters going through their training - Dominika in Russia, doing intelligence training and then going to the sparrow school, and Nate joining the CIA and going through the training. Once they meet in Helsinki things really pick up.
The time frame of the book is intended to be contemporary - Vladmir Putin is a character and he took power in approximately 1999. There were aspects of it, though, that felt very Cold War to me. In addition, the book makes the claim that Dominika was the first woman to attend Russia's spy school as a prospective agent (as opposed to as a "honeypot" who is intended to compromise men through sex). This piece of sexism gave the book a vintage feel that I wasn't ever able to wholly shake.
There were a few style quirks that I didn't like. Matthews put the pseudonyms of the spies (MARBLE, DIVA) in all caps throughout the entire book, which was distracting and unnecessary. The recipes at the close of each chapter were also distracting at the beginning, and although I began to see their value more towards the end of the book, they did nothing to advance the story and could've been left out.
In addition, Matthews gives his female spy, Dominika, synesthesia manifesting in her ability to see emotions as a colored aura. This purportedly makes her able to discern when people are telling the truth vs. lies, and the "good" people have auras with pretty colors, while the "bad" people have auras that are ugly colors like baby puke yellow. I feel like the book would've been stronger without this fanciful aspect because it was pretty dumb, honestly.
They actual "spy" part - or as the book calls it "tradecraft" - was convincing and many of the details were fun to read. Matthews is former CIA, and his descriptions were authentic. Some of the reviewers mentioned the explicit sex in the book - I didn't really find it all that explicit, although there was a lot of violence, and some sexual violence. The sexual violence was far less prevalent in Red Sparrow than in the Millennium trilogy (Girl with the Dragon Tattoo, etc) by Stieg Larssen.
The book does end in a bit of a cliff-hanger, with Dominika disappearing into Russia. There was enough of an ending that I'm not going to go directly to book 2, although I want to read the entire series. I am also looking forward to the movie.