Abstract: Identifying the principles that govern the emergence of organisation in non-equilibrium systems remains a central challenge of modern soft matter and physical chemistry. In a living cell, non-equilibrium conditions are necessary for functionality and are maintained by chemical gradients and mechanical forces. These conditions drive the reversible assembly of molecules into large-scaled functional structures that produce work needed for cellular trafficking, motility, division, and healing. When molecular assembly occurs without energy input, irreversibly, severe pathologies can occur. Today I will present our research on computational modelling of molecular self-assembly processes, in healthy and diseased states. I will discuss the example of active elastic filaments (ESCRT-III) that dynamically change their geometries to reshape and cut cell membranes. I will present comparisons of our simulation results to cell reshaping processes across evolution — from cellular trafficking in eukaryotes to cell division in archaea. I will then discuss our work on modelling pathological amyloid aggregation involved in neurodegenerative disorders, which occurs via passive nucleation and self-replication processes. I will finish with our recent efforts in computationally evolving assemblies to perform a desired function.