Today I will present our recent research on the computational modelling of energy-consuming processes that dynamically reshape and cut cells across evolution. I will first discuss the physical mechanism of filaments that drive cell division and cell trafficking in archaea and eukaryotes. I will then discuss the physical mechanism behind the dynamic self-organisation of biochemically active FtsZ filaments in the early stages of bacterial division. Throughout, I will present the comparisons of our models to in vitro and in vivo data. I will finish up with our recent thoughts on the shapes of symbiotic organisms that might have led to the emergence of eukaryotes.