Specifically, this thesis focuses on dilute solutions of high molecular-weight polymers which are widely employed as rheological modifiers, where they experience extreme shear flows that induce nonlinear chain deformations, often leading to mechanical degradation and a consequent loss in viscosity enhancement. A molecular-level understanding of how polymer architecture governs chain deformation under flow remains limited, primarily due to the scarcity of experimental techniques capable of probing scission in situ. While single-molecule microscopy methods have successfully visualized deformation in certain biopolymer systems, such approaches are not feasible for conventional synthetic polymers subjected to high shear rates. To address this gap, this thesis investigates the influence of complex polymer topology on flow-induced deformation using novel in situ small angle neutron scattering measurements in a newly developed capillary rheometer capable of accessing extreme shear rates (>10^4 1/s). This capillary rheo-SANS setup enables simultaneous characterization of both structural and rheological responses under flow. The resulting scattering data are analyzed using a newly developed framework - the Gram-Charlier Analysis of Polymer Scattering (G-CAPS) which extracts detailed information of the polymer conformation directly from scattering measurements by utilizing the well-established Gram-Charlier expansion scheme. In strongly nonlinear flows (such as those probed here), polymer chains deviate from Gaussian statistics, and G-CAPS quantifies these non-Gaussian deformations through higher-order moments of the polymer segment density distribution. The method is first validated using synthetic data generated by Brownian dynamics simulations, and subsequently applied to interpret capillary rheo-SANS measurements on topology-controlled polymers at high shear rates. The moments of the polymer distribution extracted from the scattering thus fingerprints structural changes in flow and provides a way to systematically study the influence of chain topology and finite extensibility influence on polymer deformation dynamics. We found that while finite extensibility primarily governs the stretching response of linear polymers, star polymers exhibit more complex dynamics, where synchronized arm motion and enhanced local stretching near the rigid core play a dominant role in determining their alignment in flow. Thus, the capillary rheo-SANS technique together with the G-CAPS framework provide powerful new tools to probe and engineer the molecular rheology of polymer fluids, enabling the optimization of their performance and durability across diverse applications.