We will consider a type of cooperative nonlinear elliptic system in R^N. The interest of this problem is based on the presence of Sobolev or Sobolev-Hardy critical power nonlinearities and a nonlinear coupling, possibly critical, as well as singular potentials of Hardy type. Using variational methods we will focus on the existence of bound and ground states of the underlying energy functional. Finally, for a certain range of parameters, we derive some qualitative properties and a classification criterion. This seminar is based on some works in collaboration with Angel Arroyo (UA), Eduardo Colorado (UC3M), Francesco Esposito (UNICAL) Alejandro Ortega (UNED) and Berardino Sciunzi (UNICAL).