We review the recent construction and basic properties of a refinement of sutured Floer homology given by the authors in [1], defined for weakly balanced sutured manifolds (X, τ), and provide calculations that illustrate the differences from the original construction by Juhasz [9]. For any weakly balanced sutured manifold (X,τ) we construct an algebra A_τ associated to its boundary and introduce a chain complex CF(X,τ) with coefficients in A_τ. The filtered chain homotopy type of CF(X,τ) is an invariant of the sutured manifold (X,τ). In this paper we review some of the results from [1], on which the second author spoke at 2013 Gökova Geometry/Topology Conference.