Summarizing

Summarizing is a complex task that we often ask our students to perform in order to demonstrate their understanding.  As I was reading Reading for Understanding  today, I came across this nugget:

"To summarize well, students must first comprehend what they have read and then make decisions about what is important and not so important in a text and what kinds of relationships have been represented."

While reading this, it struck me that I have given little thought to what I am truly asking from my students when I require summarizing.  I do think they have the ability to summarize but I wonder what kind of instruction and modeling would be helpful to support them in making well crafted summaries.