qgis - How to determine which polygons, if any, points fall within?

I am a amateur at GIS and need some help. I have a group of shapefiles of various areas and an Excel spreadsheet of addresses I have geocoded to points. I want to determine whether each point falls within the boundary of a shapefile, and which feature within the shapefile it falls within.

For example I have:

Shapefile Zone: polygons Zone #1, Zone #2, Zone #3, etc.
Shapefile Area: polygons Area #1, Area #2, Area #3, etc.
Shapefile Address: points Address #1, Address #2, Address #3, etc.

For my results I would like it to list:

 Address           Falls within feature
Address #1     Zone #2, Area #1
Address #2     Does not fall within any feature

Address #3     Zone #3

I know how to incorporate all the polygon features into a shapefile but not how to have it identify what polygon features of the shapefile each point falls into.

I am using ArcGIS and Quantum GIS. So in summary my issue is taking coordinates and determining if they fall within certain polygon shapefiles I have. The goal in the end is to start with a list of geocoded addresses (points) and end with a determination of which (if any) polygon's each point falls in.