In 1982 Beilinson, Bernstein and Deligne have proved that the heart H(X,Y) of a faithful torsion pair (X,Y) is an abelian category. In 2009 Colpi and Gregorio have proved that H(X,Y) is a Grothendieck category if and only if the torsion free class Y is cogenerated by a 1-cotilting module. Recently in a joint paper with Colpi and Mantese we have found necessary and sufficient conditions for H(X,Y) to be equivalent to a module category. In this talk I will describe the results obtained.