Soft matter (colloids, polymers, proteins…) often self-assembles into gels with diverse structure and mechanics, ubiquitous in nature and extensively used to improve diverse industrial products, where they provide texture, softness, and stability. Through the interplay between their microstructure with an imposed deformation, they can be stretched, flow, squeezed or fractured, but controlling and being able to design such processes (think for example to soft inks for 3D printing technologies) requires a fundamental understanding that is still lacking. We have developed a theoretical/computational approach that addresses in particular the role of the network topology in such materials, its stress-controlled evolution over time and its implications for the mechanics. I will give an overview of the novel insight gained into the time evolution of the material properties due to aging, the origin of the uniquely wide-ranged viscoelastic spectra and the presence of a topologically controlled softness in gel networks. I will discuss how our findings can help understand the nontrivial mechanical response of soft gels in different contexts, develop constitutive models and theories further, design smart materials.