Keynote won't update

I'm trying to update my version of Keynote to 6.6.1 (it's now 6.2.2) so I can open presentations created in newer versions, but every time I click the "update" button on the App Store, all I get is the spinning wheel thing in the top left corner, which says "checking for updates" by it. Nothing downloads, nothing happens. Any suggestions?

I've just updated to El Capitan 10.11.3

Most likely this is down to the fact that your OS is not updated. The current version of Keynote requires macOS 10.12. You can confirm this by deleting Keynote from your applications folder, starting AppStore and installing Keynote. You will get an error message that a later version of your operating system is required.