In this thesis, we study the structure-function relation of colloidal gels, a class of soft materials. We combine simulations and experiments to obtain insights into the microstructural response of colloidal gels in the presence or absence of external stress. Specifically, we take a closer look at processes such as fatigue, shear and gravitational collapse and study how deformation or gravity affect the microstructure and network topology of these particle gels. We employ a recently developed particle system, which can be index- and density matched using non-hazardous polar solvents, to image large volumes of colloidal gels. This confocal microscopy data allows us to determine the network topology of these particle gels using a topology mapping algorithm described in this thesis. Simultaneously, we perform simulations to obtain a better understanding of changes in the network topology of colloidal gels during deformation.