When searching on date fields there is a keyword QUERY_DATE which signifies the day when the search is being run. A saved search with QUERY_DATE will not search for a particular date, instead the search date will match the day that the search is run.
This is useful if you want to save a search for everything happening today e.g. all diary tasks due for a particular person today. You can even use QUERY_DATE with modifiers, or as part of a range. For example, you can search for <=QUERY_DATE to find everything with dates including and prior to today, or QUERY_DATE ... QUERY_DATE + 365 to find all dates occurring in the next year.
A search using QUERY_DATE to find anything with a due date before today, with Paul Rowe as the responsible person.