You can see invoices that are outstanding on the main Invoices Grid in the Transactions & Invoices Module. Rows highlighted in red have no payments yet, those highlighted in orange have partial payments and those shown as blue/black are fully paid. You can also see the status of invoices for each constituent in their record under their Invoices Tab. 

You can sort the grid by Status Column and Filter Is Equal to "Unpaid" OR Is Equal to "Partially Paid" to create a list of all outstanding invoices. You can also use the side bar to filter by date ranges.