<p dir="ltr">In this dissertation, I use methods of theoretical physics to study principles governing the stochastic dynamics of living timekeepers in a few different contexts. First, focusing on the phenomenon of stochastic growth and division processes in the simplest living organism (the bacterial cell), I present a procedure for analyzing high-throughput, high-precision dynamic datasets to identify emergent simplicities, in particular scaling laws, that provide new insights into a long-standing problem (that of cell size homeostasis). Recasting the question from a stochastic, intergenerational viewpoint (i.e., one that considers the entire life histories of individual cells without recourse to a priori mechanistic assumptions), and taking advantage of identified emergent simplicities to achieve dimensional reduction of the problem, permits a reformulation that captures the inherent stochasticity of individual cells. Identification of discrete modes by which homeostasis is maintained---in particular, via reflexive (elastic) adaptation of cell size and reflective (plastic) adaptation of growth rate---provides important insights into key system constraints that govern living bacterial cells, with additional implications for the design of functional adaptive synthetic homeostats. The observation of non-Markovian dynamics in single-cell growth rates implies the existence of intergenerational memory and plastic adaptation in these simple organisms. I also present my work on the process of early endosomal maturation in human cell lines, multi- fork DNA replication in Escherichia coli cells, and a physics principle and theory predictions for emergent periodicity in a decentralized follow-the-leader dynamic in a collective of randomly signaling agents. This body of work provides mechanistic insights into how temporal organization in outcomes emerges despite the inherently stochastic nature of the constituent dynamics, with each system adopting its own mechanism to achieve this universal goal.</p>