Aneuploidy has historically been associated with detrimental phenotypes and diseases, notably cancer and Down Syndrome. However, recent experimental evidence suggests aneuploidy provides adaptation to numerous stressors, including drug resistance, making aneuploidy study critical to biomedical research. However, the molecular mechanisms underlying this process remained elusive until now. This work focused on exploring several approaches to understanding those mechanisms. Frist, we have developed a general mathematical model of organism adaptation to adverse environments. In our model, the adaptation to environments takes place as a trade-off in the space of traits, of which aneuploidy allows a more efficient and rapid sampling. This model was validated on experimental data and used to predict optimal drug combinations targeting heterogeneous populations breast tumor cells. Second, we used the framework of network biology to model biomolecular networks and apply to them results from the graph theory and existing results on weighted graphs from other domains. We were able to predict the distribution of essential genes, lethal genetic interactions and essential evolvable genes - essential genes that can be deleted in the aneuploid background. We were as well able to build a predictive model for inferring most likely pathways underlying the phenotype of large-scale genetic perturbations. Finally, we attempted to explore several possible modes besides dosage effects by which aneuploidy could impact the gene expression regulation. This required a development of an image analysis toolkit that was validated and released for as open-source software.