From the initial value problem in general relativity to binary neutron star initial data

What is the initial value problem in General Relativity and why is it so important? We review its most salient features by tracing
the historical route of the subject that led to our current understanding. Methods of solution for binary systems are presented and
emphasis is given on binary neutron star initial data since these constitute one of the most common source of gravitational waves that will be searched from the experimental community.