  We outline the basic questions that are being studied in the theory of
entanglement. Following a brief review of some of the main achievements of
entanglement theory for finite-dimensional quantum systems such as qubits, we
will consider entanglement in infinite-dimensional systems. Asking for a theory
of entanglement in such systems under experimentally feasible operations leads
to the development of the theory of entanglement of Gaussian states. Results of
this theory are presented and the tools that have been developed for it are
applied to a number of problems.
