Although microbial populations are typically described by averaged properties, individual cells present a certain degree of variability. Indeed, initially clonal microbial populations develop into heterogeneous populations, even when growing in a homogeneous environment. A heterogeneous microbial population consists of cells in different states, and it implies a heterogeneous distribution of activities (e.g. respiration, product yield), including different responses to extracellular stimuli. The existence of a heterogeneous cell population may explain the lower productivities obtained for cultivations in large-scale reactors, where substrate and oxygen gradients are observed, in comparison to cultivations in well-mixed bench scale reactors. Population balance models (PBM) have been used in a broad range of applications (e.g. crystallization, granulation, flocculation, polymerization processes) to predict distributions of certain population properties including particle size, mass or volume, and molecular weight. Similarly, PBM allow for a mathematical description of distributed cell properties within microbial populations. Cell total protein content distributions (a measure of cell mass) have been observed to provide a dynamic picture of the interplay between the cells and their surrounding extracellular environment. The work here presented aimed at developing a model framework based on PBM as a tool to further understand the development of heterogeneous microbial populations subjected to varying environmental conditions. Three cases are presented and discussed in this thesis. Common to all is the use of S. cerevisiae as model organism, and the use of cell size and cell cycle position as single-cell descriptors. The first case focuses on the experimental and mathematical description of a yeast population dynamics, in response to the substrate consumption observed during batch cultivation. Cell size and cell cycle position distributions were used to describe the cell population. A two-stage PBM was developed and coupled to an unstructured model describing the extracellular environment. The good agreement between the proposed multi-scale model and experimental data (both the overall physiology and cell size and cell cycle distributions) indicates that a mechanistic model framework is a suitable tool for describing the microbial population dynamics in a bioreactor. The second case provides an extension of the proposed model framework (PBM coupled to an unstructured model) to a continuous cultivation. A compartment model approach was applied for addressing situations where two zones (compartments) are formed due to non-ideal mixing in the bioreactor. In particular, this approach was used in order to assess the impact of the degree of compartmentalization (i.e. deviation from the ideal mixing case) on the population dynamics and overall system performance under various operation conditions (substrate feed concentration and dilution rate). It was possible to conclude that the deviation from ideal mixing may have a significant effect on the observed system dynamics. Moreover, oscillatory pseudo-steady states may be observed for particular combinations of operating conditions and degree of compartmentalization. In the third study attention was paid to the integration of the proposed model framework in a computational (CFD) fluid dynamic model. The anaerobic Growth of a budding yeast population in a continuously run microbioreactor was used as example. The proposed integrated model describes the fluid flow, the local cell size and cell cycle position distributions, as well as the local concentrations of glucose, ethanol and biomass throughout the reactor. This work has proven that the integration of CFD and population balance models, for describing the growth of a microbial population in a spatially heterogeneous reactor, is feasible, and that valuable insight on the interplay between flow and the dynamics of a budding yeast population (e.g. formation of substrate gradients and non-growth zones) is gained. In silico simulation tools, as the one proposed, may be used for hypothesis generation and testing, and when coupled to an experimental set-up may be used for process and reactor design optimization.