This talk was part of the Thematic Programme on "Non-equilibrium Processes in Physics and Biology" held at the ESI August 19 -- October 11, 2024.

Cell shape is related to many crucial biological functions. However, the cell-to-cell shape varies in tissues. Recent works show that cell shape variability in different epithelial monolayers follows a nearly universal distribution. What is the origin and implications of this universality? How does it depend on the physical conditions? I will discuss a mean-field analytical theory for cell shape characterized via the aspect ratio (AR). I will show that a single parameter, alpha, containing all the system-specific details, describes the probability distribution function of AR: this leads to a universal relation between the standard deviation and the average of AR. In addition, the cell shape in these systems also strongly correlates with the monolayer dynamics. Thus, we can describe both their static and dynamic properties via the single parameter alpha. I will finally discuss our recent works on the implications of cell shape variability for epithelial systems.