Cells that are genetically identical can exhibit differences in phenotype, however, such variation remains masked in bulk measurements. To capture variability among individual cells, as well as the behavior of subpopulations of cells, requires studies with single cell resolution. Here I will describe a new class of microfluidic devices that enables studies at the single cell level. First, I will describe a microfluidic device that enables measurements of the mechanical properties of individual cells. The ability of cells to deform through narrow spaces is central in physiological contexts ranging from immune response to metastasis. To elucidate the effect of nuclear shape on the deformability of neutrophil cells, I manipulate levels of a structural protein in the nucleus, and show this alters both nuclear shape and the ability of cells to deform through the narrow channels. These results help to elucidate the mechanism underlying nuclear shape transitions, and have implications for understanding changes in the physical properties of cancer cells. Second, I will describe a microfluidic device that enables tracking lineages of single cells. In most cases, heritable phenotypic variation arises from differences in DNA sequence, yet even cells that are genetically identical can exhibit variation in phenotype, which are critical during differentiation and development, and possibly in response to environmental stress. By studying the expression patterns of three, naturally regulated proteins in lineages deriving from single yeast cells, I show that the timescale of phenotypic variation differs markedly among the observed proteins; this is an essential step towards understanding the timescales of phenotypic variation, and correlations in phenotype among single cells within a population.