Cells with different properties grow, divide, and interact with each other and with Extra-Cellular Matrix (ECM) through mechanical forces and signal transduction, resulting in the formation of complex patterns that are important for processes such as tissue development and wound healing. However, current computational cell models are challenged to account for detailed changes in cellular shapes and physical mechanics when studying thousands of migrating and interacting cells. We discuss recent development of quantitative models and algorithms, with focus on a novel dynamic cellular finite element (dyCelFEM) model. With full account of changes in cellular shapes, cellular topology, and celluar mechanics, and with keyintra-cellular signaling networks embedded in individual cells, we can study the full range of cell motion, from motilities of individual cells to collective cell migrations. We discuss our recent findings on effects of micro-patterned geometry on cell elongation and migration. We also described results on examining the effects of biochemical and mechanical cues in regulating cell migration and proliferation, and in controlling tissue patterning in re-epithelialization of skin wound healing (Joint work with Jieling Zhao, Youfang Cao, Wei Tian, Luisa DiPietro, and Margaret Gardel).