This is a re-read for me of a book in my collection. Meyendorff's Byzantium and the Rise of Russia is rightly considered a classic in the history of orthodoxy and of Russia. Meyendorff's aim is to consider the role that the fading Byzantine Empire had in the rise of Moscow as the dominant power in Russia during the 14th and 15th century and in the preservation of the unity of the Metropolitate of the Rus (theoretically based in Kiev, but, really, highly itinerant). These two campaigns mutually influenced each other and served as a means to define Moscow's vision of the newly liberated (from Tatar control) Russian state.
Meyendorff's main argument is to argue that the Byzantine and Italian influence tended to favour Moscow's initial collaboration with the Tatars and, eventually, their succession from them. In addition, the Patriarch of Constantinople continued to pursue a policy of maintaining one metropolitanate, largely under Moscovite influence, of the Rus in the face of Lithuanian/Polish attempts to create a separate Metropolitanate for the Orthodox in their territory. Central of Meyendorff's argument is the assumption that the Byzantines were trying to maintain a 'Byzantine Commonwealth' made up of the major Slavic Orthodox states in the Balkans and beyond. This 'Commonwealth' pursued a very similar religious policy, even if its political coherence is, at least, questionable. This notion, popularized by Obolensky, has come into disrupte in recent years as imprecise, so it can be a distracting element of this book.
My own background to late mediaeval and early modern Russia is slim- limited to an undergraduate Russian history course more than twenty-five years ago. It was interesting to revisit old ground, but I'm not sure if I'm qualified as a judge of that aspect of the book. For Byzantine studies, this book is a classic, but it is beginning to get a bit long in the tooth. Useful still, but should be used with some caution.