While running through some SalesForce training (mostly on TrailHead) I suddenly found lots of pages were coming up blank.

The menus seemed to work, and switching to Classic worked, but some of the pages I needed were Lightning-specific.
Inspecting the pages turned up
DOMException: Failed to read the 'sessionStorage' property from 'Window': Access is denied for this document
Searching around on that and thinking about access/permissions issues, I found that whitelisting cookies for the SalesForce sites resolved the issue.
If you’re using Chrome, open settings and click on “Cookies and other site date” under “Privacy and security.”

Then under “Sites that can always use cookies” add
https://[*.]my.salesforce.com
https://[*.]lightning.force.com
flagging them for “All cookies, on this site only”

I think a Chrome update came out that changed the default for third party site cookies which caused the problem. This resolved it for me.