Evolutionary dynamics are controlled by a number of driving forces, such as natural selection, random genetic drift and dispersal. In this perspective article, we aim to emphasize that these forces act at the population level, and that it is a challenge to understand how they emerge from the stochastic and deterministic behaviour of individual cells. Even the most basic steric interactions between neighbouring cells can couple evolutionary outcomes of otherwise unrelated individuals, thereby weakening natural selection and enhancing random genetic drift. Using microbial examples of varying degrees of complexity, we demonstrate how strongly cell-cell interactions influence evolutionary dynamics, especially in pattern-forming systems. As pattern formation itself is subject to evolution, we propose to study the feedback between pattern formation and evolutionary dynamics, which could be key to predicting and potentially steering evolutionary processes. Such an effort requires extending the systems biology approach from the cellular to the population scale.This article is part of the theme issue 'Self-organization in cell biology'.