Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this talk I will discuss a series of individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and their corresponding population-level partial differential equation formulations. I will demonstrate the ability of these models to predict the population-level response of a cell spreading problem for both proliferative and non-proliferative cases. I will also discuss the potential of the models to predict long time travelling wave invasion rates.