Explore mathematical modeling approaches to understand collective cell motion in this colloquium lecture by Philip K Maini from the University of Oxford. Discover how mathematical models can illuminate the complexities of collective cellular behavior across diverse biological contexts including developmental biology, wound healing, and cancer growth. Learn about the mathematical challenges inherent in modeling these complex biological processes and examine specific examples from cancer cell invasion and developmental biology research. Investigate a range of modeling approaches from fully nonlinear coupled systems of partial differential equations to hybrid agent-based models, understanding how different mathematical frameworks can capture various aspects of collective cellular dynamics and provide insights into fundamental biological processes.