Abstract: In this talk I will review some of the recent developments of reformulating Quantum Field Theory in terms of novel geometric structures. Concretely, I am going to motivate how the dual formulation of scattering amplitudes in planar N=4 sYM theory in terms of on-shell diagrams, the positive Grassmannian and its uplift into the amplituhedron naturally leads to the appearance of differential forms with logarithmic singularities. In certain cases, these dlog-forms directly translate into new dlog representations of Feynman loop integrals. I will discuss the special properties of these dlog integrals and introduce some new insights into integrating these forms directly.