As part of its Google Takeout service, Google now allows users to download their Gmail and Google Calendar data. You can save all or just some of your email and appointments—the former in MBOX format, the latter in ICS (iCalendar)—right alongside any other Google Takeout archives you desire, including your data from Google+, YouTube, Contacts, Drive, Voice, your Google profile, your Google location history and Google Hangouts.
Archives for Google Calendar are available immediately, while downloads for Gmail will be rolling out sometime this month.
