Yes! Pillow allows you to export your entire database as well as the sound recordings.
Exporting your database
You can export your database in .txt format while Pillow Premium also supports sleep database export to a .csv file. The resulting file contains sleep quality percentage, sleep start and end times, time in each sleep stage (Awake, REM, Light, Deep), the number of sounds recorded and wakeup mood for each sleep session (when mood was provided).
To export your sleep database:
Open Pillow on your iPhone or iPad
Tap on the 'Settings' icon at the top right corner
Scroll down and find "Data & Services"
Tap on "Manage data"
Select the export method you prefer for the data you wish to export
Exporting your sound recordings
Pillow currently allows you to export your sound recordings by sending them as an email attachment.
To export a sound recording:
Open Pillow on your iPhone or iPad
Tap on the 'Settings' icon at the top right corner
Scroll down and find "Data & Services"
Tap on "Manage data"
Select the "Export audio recordings" option