We give a brief introduction to current practices in cafe-style espresso extraction. Making the tastiest cup is considered an art rather than a science, however, processes can be made more systematic by better understanding the physical processes underlying brewing. We develop a physics-based mathematical model for the extraction process. Owing to the disparity in lengthscales between that of a grain within the “puck” and the depth of the whole “puck”, the model can be systematically reduced via asymptotic homogenisation. The reduced model can then be solved by numerical methods. We will show that the model is able to reproduce some of the trends that are observed in experimental data and in practice. We also discuss possible strategies to make espresso more efficiently and more reproducibly.