Found a hacky way, using substring of FileRef:

/sites/mysite/_api/web/lists/getbytitle('Useful Links')/items?$filter=substringof('Useful Links/My Folder/', FileRef)

Found a hacky way, using substring of FileRef:

/sites/mysite/_api/web/lists/getbytitle('Useful Links')/items?$filter=substringof('Useful Links/My Folder/', FileRef)

Or, with sp-rest-api.js:

var api = new SpRestApi({
    listTitle: 'Useful Links',
    onsuccess: console.log,
});

api.getAllItemsFromListSubfolder('My Folder');