At Amazon's launch event today in Seattle the company announced its first DVR called the Fire TV Recast. There's no cable TV tuner built-in, so the channels available will be the ones you can access with a connected over-the-air antenna (like ABC, CBS, FOX, NBC, PBS or the CW).
Also, since the Recast doesn't plug directly into a TV, you can place it anywhere in your house to get the best reception, which the app can also help you determine. It then beams your recorded shows or live TV anywhere through your home to an Echo Show, Fire tablet, mobile device (iOS or Android with the Fire TV app) or a Fire TV device. You can also take your recordings on-the-go with the Fire TV app.