Viruses; Genisis and Taxonomy

[AJ Boulay]

As a student of biology, I am curious about the replication and 
classification of viruses.

I understand that viruses are inert until they infect a host, that they 
do not undergo replication or division, etc. 

This leads to my question: How then do viruses proliferate? I can see an 
infected cell within the host replicating, but is this infected cell 
considered a "virus"? With this in mind, can viruses be classified as an 
organism at any time in thier life cylce?

Thanx,

AJ