The actin cytoskeleton is a dynamic structure that constantly undergoes complex reorganization events during many cellular processes. Mathematical models and simulations are powerful tools that can provide insight into the physical mechanisms underlying these processes and make predictions that can be experimentally tested. Representation of the interactions of the actin filaments with the plasma membrane and the movement of the plasma membrane for computation remains a challenge. Here, we provide an overview of the different modeling approaches used to study cytoskeletal dynamics and highlight the differential geometry approach that we have used to implement the interactions between the plasma membrane and the cytoskeleton. Using cell spreading as an example, we demonstrate how this approach is able to successfully capture in simulations, experimentally observed behavior. We provide a perspective on how the differential geometry approach can be used for other biological processes.