There are many ways to read comic books, and one of those that has become more common in recent years is on a computer. Peruse was created as a way to make exactly that as easy and pleasant as possible, and to simply get out of the way and let you read your comic books. One could say that it allows you to peruse your comic books at your leisure, but that would be a silly way of putting it - so, peruse your comic books at your leisure!
One of the ways in which Peruse ensures your reading experience is as pleasant and effortless as possible is to allow you to simply pick up where you last left off. The welcome page in the application (first screenshot below) shows you your most recently read comics, and shows your progress through them. To pick up where you left off, simply tap the top left item and you will be taken right to the page you were reading before you had to stop.