We outline the current status of the differential expansion (DE) of colored knot polynomials i.e. of their Z–F decomposition into representation– and knot–dependent parts. Its existence is a theorem for HOMFLY-PT polynomials in symmetric and antisymmetric representations, but everything beyond is still hypothetical – and quite difficult to explore and interpret. However, DE remains one of the main sources of knowledge and calculational means in modern knot theory. We concentrate on the following subjects: applicability of DE to non-trivial knots, its modifications for knots with non-vanishing defects and DE for non-rectangular representations. An essential novelty is the analysis of a more-naive Z–FTw decomposition with the twist-knot F-factors and non-standard Z-factors and a discovery of still another triangular and universal transformation V, which converts Z to the standard Z-factors V−1Z=Z and allows to calculate F as F=VFTw.