As infectious agents of bacteria and vehicles of horizontal gene transfer, plasmids play a key role in bacterial ecology and evolution. Plasmid dynamics are shaped not only by plasmid-host interactions but also by ecological interactions between plasmid variants. These interactions are complex: plasmids can co-infect the same cell and the consequences for the co-resident plasmid can be either beneficial or detrimental. Many of the biological processes that govern plasmid co-infection-from systems that exclude infection by other plasmids to interactions in the regulation of plasmid copy number-are well characterized at a mechanistic level. Modelling plays a central role in translating such mechanistic insights into predictions about plasmid dynamics and the impact of these dynamics on bacterial evolution. Theoretical work in evolutionary epidemiology has shown that formulating models of co-infection is not trivial, as some modelling choices can introduce unintended ecological assumptions. Here, we review how the biological processes that govern co-infection can be represented in a mathematical model, discuss potential modelling pitfalls, and analyse this model to provide general insights into how co-infection impacts ecological and evolutionary outcomes. In particular, we demonstrate how beneficial and detrimental effects of co-infection give rise to frequency-dependent selection on plasmid variants. This article is part of the theme issue 'The secret lives of microbial mobile genetic elements'.