Remove-item recursive

How do you delete all the txt files from one folder and all sub folders?

remove-item -Path Logs -Filter *.txt -Recurse

This works but it tries also to delete the subfolders and raises some exceptions

remove-item -Path Logs\* -Filter *.txt -Recurse

This doesn't delete the txt files in the subfolders

remove-item -Path Logs -Include *.txt -Recurse

This does exactly nothing, most probably because the Path has no wildcard

remove-item -Path Logs\* -Include *.txt -Recurse

It seems a simple task, but it doesn't, so I tried all the combinations of path with include and filter but no one really works, what I missing?