I would like to see some Advanced search functionality, such as:
Show all payments to Payee X from Accounts A and B in a given time period and within categories 1, 2 and 3, broken down by months. The result should show a total and a possibility to export.
You can achieve this to a degree using reports, especially custom reports. You could export a report that you've generated to a CSV file and search further from there.
I'll note your feature request here and leave it open to see how many votes this dedicated support for this feature gets.