Tolstoy's massive novel, like Victor Hugo's Les Miserables, is a classic that, despite being written in a foreign language over a century ago in a format that would be unpublishable today, continues to be read and enjoyed.
The differences between his characters and American readers of today are chasmic. They are aristocratic, we have been raised in a society of unbridled equality. Many of them, especially the young ones, possess a worshipful love for their ruler and their country, while many of us consider our ruler one of the worst Americans ever born. (If he's even American, which we very much doubt.)
To top it all off, Tolstoy intersperses his story with essays about his theories and opinions on military history, strategy, and patriotism. A modern author trying to publish a book containing even one such essay would have it promptly edited out, if he even got that far. In a culture of abbreviations and shorthand, we have lost all patience for opinions that are not enshrouded in entertainment. We have Internet and status updates and all our information comes in little pieces. We don't have time for long books.
And yet War and Peace has not disappeared. Apparently some things are timeless. The questions: "What is love?" and "What is our purpose?" are still being asked. No matter who we are or what culture we are products of, we will always understand those questions.