Collective tissue dynamics, more specifically a tissue\u27s ability to fluidize and segregate, is imperative for proper embryonic development and normal physiological functioning. In this thesis, I use vertex models to understand how cell-scale properties govern large-scale collective behavior. I begin with the process of fluidization in ordered monolayers. By perturbing beyond the linear regime, I show that in confluent tissues the linear response does not correctly predict the non-linear behavior, which, in this case, is the ability to exchange neighbors and fluidize. We also construct a simple analytic ansatz that can predict the non-linear behaviour responsible for cellular motion in tissues. Shifting from fluidization to segregation, I next focus on two-dimensional (2D) binary mixtures. I show that a difference in cellular shape or size is insuffcient to induce an emergent interfacial tension, and this leads to large-scale mixing. However, shape disparity can induce a small-scale demixing over a few cell diameters. We report a very similar de-mixing observed in an experimental co-culture of differently shaped Keratinocytes. This can be understood by examining the non-reciprocal energy barriers for neighbor exchanges at the interface, leading to micro-segregation. We next move on to three-dimensional (3D) binary mixtures that have an explicit interfacial tension between two distinct cell types. We find that they can undergo complete segregation, imparting unique geometric properties to cells at the interface. To understand the feedback between interfacial tension and cellular geometry, we develop simple toy models to probe the system\u27s response to perturbations in cellular topology along the interface. Neighbor exchange processes in confluent tissues also involve perturbing the underlying topology with neighboring cells, and therefore are heavily regulated by the cell shape and inhomogeneity in surface tension. In all of the above cases, these local barriers govern the onset of unique collective behavior like-fluidization, microdemixing and novel geometric signatures
