Forms submissions can be saved to many places. For instance you can save your submissions in the Live Forms server's built-in submission repository; store them as email attachments in someone's email inbox; store them into a Google Sheets or a Google Drive folder; store them into a document management system or ECM system such as Confluence; store them into a database or other 3rd party system such as a CMS etc. The options are really endless.
The Live Forms server currently supports basic reporting which enables you to view the submissions activity over a given time period via the submissions repository UI page.
Also refer to Report options.