Understanding eco-evolutionary dynamics in cancer tumors, species invasions, and the human microbiome is vital for numerous health and economic applications. However, spatial structure and population heterogeneity make this challenging. This dissertation tackles these challenges using a population dynamics approach, wherein systems evolve through individual growth and dispersal. The bulk of this dissertation studies expanding populations, such as growing microbial colonies, species range expansions, and cancer tumors. In this context, I first study the effect of a directional bias in dispersal: I develop a model for the stochastic growth of left-right or chirally asymmetric cells that quantitatively reproduces experimental patterns in microbial colonies. Using the model, I demonstrate that chiral dispersal provides an evolutionary advantage and affects spatial population structure in expanding populations. Second, I investigate the impact of environmental structure affecting both dispersal and growth on expanding populations. I show that cooperative population expansions in a periodic environment can be pinned to a particular location or locked to specific velocities determined by the environmental periodicity. Third, I study the problem of a phenotypically heterogeneous population, with each phenotype differing in growth and dispersal abilities. I determine the exact velocity of an expanding population where phenotypes move ballistically and explain the connection to the explosive growth transition in experimental microtubule asters. The final chapter of the dissertation examines the challenge of assembling microbial communities for performing functions such as biofuel production, nitrogen fixation, or health remediation. Due to the exponential number of possible species combinations, bioengineers resort to heuristic search strategies to find the optimal community. I identify biological properties and develop statistical measures to help bioengineers estimate their chance of success in assembling an optimal community. / 2023-02-06T00:00:00Z