Technological advances in molecular biology over the last several decades have enabled researchers to probe the inner workings of living systems at unprecedented scale and resolution. These new capabilities have resulted in the emergence of the field of quantitative biology, which seeks to utilize mathematical modeling along with techniques from systems biology and synthetic biology in order to ascertain the design principles that underlie the structure and function of biological regulatory networks. In pursuit of this goal, it has become clear that heterogeneity at the single-cell level and the dynamics, or time-dependent behavior, of these networks are critical features of a multitude of biological processes. Much of the foundational work establishing the importance of these themes began from the study of microbes such as the budding yeast Saccharomyces cerevisiae. However, even in unicellular organisms such as S. cerevisiae, significant challenges remain in tracking and analyzing single cells over long periods of time, as well as monitoring gene expression dynamics at scale. Development of these capabilities is critical, not only for understanding the cell biology of S. cerevisiae, but also for being able to apply the mechanistic insights obtained from yeast to evolutionarily conserved pathways in higher eukaryotes. In this thesis, I describe the design and application of microfluidic technologies for S. cerevisiae that address these limitations. In Chapter 1, I detail the utility of microfluidic devices and time-lapse fluorescence microscopy for analyzing single cells and recording biological dynamics. In Chapter 2, I describe the development of novel microfluidic devices that enable long-term isolation and tracking of single yeast cells, culminating in a design that can monitor cells over the course of their entire replicative lifespans. In Chapters 3 and 4, I discuss applications of the microfluidic technologies described in Chapter 2. Chapter 3 concerns the discovery of metabolic cycles in flavin fluorescence at the single-cell level, which can oscillate along with and independently of the cell division cycle, persisting even when cellular respiration is blocked. Chapter 4 describes the uncovering of two divergent paths taken by single yeast cells during replicative aging, in which distinct dynamics of heterochromatin silencing at the rDNA region that modulate cellular lifespan can be detected in each group. In Chapter 5, I apply the design principles validated in the construction of microfluidic devices for tracking single cells in order to develop a high-throughput microfluidic platform for recording gene expression dynamics of thousands of yeast strains simultaneously. I demonstrate a proof-of-principle of this technology by monitoring changes in gene expression across more than 4000 yeast strains in real-time during the diauxic shift. The microfluidic devices developed and described herein underscore the importance of single-cell analysis and dynamics-based regulation by elucidating novel sources of heterogeneity at the single-cell level and demonstrating how metabolic, chromatin silencing and gene expression dynamics contribute to the regulation of complex processes such as cell division, replicative aging and growth in changing environments. Further, these technologies establish a foundation upon which future studies can continue to pursue quantitative biology work in yeast, from the single-cell level to the genome scale.