  The separability problem is one of the basic and emergent problems in the
present and future quantum information processing. The latter focuses on
information and computing based on quantum mechanics and uses quantum bits as
its basic information units. In this paper, we present an overview of the
progress in the separability problem in bipartite systems, more specifically in
two quantum bits systems from the criterion based on the inequalities of Bell
in $1964$ to the recent criteria of separability in 2018.
