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 wake-up 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
Currently, Pillow allows you to export your sound recordings by sending them as email attachments or through other means.
To export your sound recordings:
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.