Im looking for a way to setup a lil' script that will read the output from a command and dump certain items from that into another file

for an example, im trying this
cat test | grep "statement" > test.answer

but its giving me the full line that it finds
is there any way to take out a portion of text from before what i want and after what i want?

as in, I am searching for address=here
so i: cat test | grep "here" > test.answer
and i want to get rid of the parts before and after the word 'here'...is there anyway to do this?

Thanks
David