What do we need to store for shadow volumes and shadow mapping... I understand that shadow volume use the ray of light shooting all edges of each object. Do we store all the vertices that defined the plane away from the light source and form a list of planes used to test the other objects are in shadow. Shadow mapping: Do we store an 2D arrays of data for each light sources and use it to map with the object?

Maybe these will help:

Shadow Volumes
Shadow Mapping

A nice summary of multiple techniques:

http://developer.download.nvidia.com/presentations/2008/GDC/GDC08_SoftShadowMapping.pdf