how to handle large file uploads reliably

We're trying to build a system that can deal with users uploading really big files, like gigabytes worth. We're using cloud storage already, but I'm curious about the best ways to make sure these uploads are dependable and can be picked up again if they stop. Have you seen any good ways to handle large file uploads, especially when the network goes down or things mess up on the user's computer? Any particular services or methods you'd suggest?