classical mechanics - What is the difference between configuration space and phase space?

1. 
   

   What is the difference between configuration space and phase space?

   
   
   


2. 
   

   In particular, I notices that Lagrangians are defined over configuration space and Hamiltonians over phase space. Liouville's theorem is defined for phase spaces, so is there an equivalent conservation law for the configuration space?

   
   


3. 
   

   In the process of modeling a physical system, when it is appropriate to use one instead of the other?