Light scalar fields such as axions and string moduli can play an important role in early-universe cosmology. However, many factors can significantly impact their late-time cosmological abundances. For example, in cases where the potentials for these fields are generated dynamically --- such as during cosmological mass-generating phase transitions --- the duration of the time interval required for these potentials to fully develop can have significant repercussions. Likewise, in scenarios with multiple scalars, mixing amongst the fields can also give rise to an effective timescale that modifies the resulting late-time abundances. Previous studies have focused on the effects of either the first or the second timescale in isolation. In this thesis, by contrast, we examine the new features that arise from the interplay between these two timescales when both mixing and time-dependent phase transitions are introduced together. First, we find that the effects of these timescales can conspire to alter not only the total late-time abundance of the system --- often by many orders of magnitude --- but also its distribution across the different fields. Second, we find that these effects can produce large parametric resonances which render the energy densities of the fields highly sensitive to the degree of mixing as well as the duration of the time interval over which the phase transition unfolds. Finally, we find that these effects can even give rise to a "re-overdamping" phenomenon which causes the total energy density of the system to behave in novel ways that differ from those exhibited by pure dark matter or vacuum energy. All of these features therefore give rise to new possibilities for early-universe phenomenology and cosmological evolution. They also highlight the importance of taking into account the time dependence associated with phase transitions in cosmological settings. In the second part of this thesis, we proceed to study the early-universe cosmology of a Kaluza-Klein (KK) tower of scalar fields in the presence of a mass-generating phase transition, focusing on the time-development of the total tower energy density (or relic abundance) as well as its distribution across the different KK modes. We find that both of these features are extremely sensitive to the details of the phase transition and can behave in a variety of ways significant for late-time cosmology. In particular, we find that the interplay between the temporal properties of the phase transition and the mixing it generates are responsible for both enhancements and suppressions in the late-time abundances, sometimes by many orders of magnitude. We map out the complete model parameter space and determine where traditional analytical approximations are valid and where they fail. In the latter cases we also provide new analytical approximations which successfully model our results. Finally, we apply this machinery to the example of an axion-like field in the bulk, mapping these phenomena over an enlarged axion parameter space that extends beyond those accessible to standard treatments. An important by-product of our analysis is the development of an alternate "UV-based" effective truncation of KK theories which has a number of interesting theoretical properties that distinguish it from the more traditional "IR-based" truncation typically used in the literature.