Most of the time you use one-to-many and many-to-many relations. As of 3.4 RedBeanPHP offers limited support for other relations as well.
One-to-one relations are not used frequently. Traditional 1-1 records are linked by their primary keys. In RedBeanPHP you can load them like this:
list($author,$bio) = R::loadMulti('author,bio',$id);
This loads an author and a biography with the same ID. You need to make sure the IDs are in sync yourself, you can use transactions for this. Note that real one-to-one relations are rare and most of the time they represent legacy records. Also consider using a simple own-list instead of a real one-to-one or just put the records in the same table.
Relational database are not suitable for polymorph relations. However if you ever need to load a bean of which the type is based on a field value you can use a slight variation of fetchAs():
$ad = $page->poly('contentType')->content;
Returns the bean referred to in content_id using the bean type specified in content_type. If content type contains the value 'advertisement' the content will be a bean with type 'advertisement' and id = content_id.
RedBeanPHP Easy ORM for PHP © 2013 Gabor de Mooij and the RedBeanPHP community - Licensed New BSD/GPLv2