Is there a way to have an edit button on any content which the logged in user has permission to edit, including their own profile?

If I am logged in as an administrator, I get the contextual edit buttons an all blocks and nodes and can edit. If I am logged in as a user with less permission, but still enough to edit that content, those buttons aren't there. There are also no edit buttons on the user profile pages for any types of user, so if you are not an admin, you cannot easily edit this. I was hoping for a way to either turn on the contextual admin style pencil buttons for all users with permission to edit a specific bit of content, or at least be able to add my own buttons in the node or user template if allowed.