Aneuploidy, an abnormal chromosome composition, results in a stoichiometric imbalance of protein complexes, which jeopardizes the fitness of aneuploid cells. Aneuploid cells thus need to compensate for the imbalanced DNA levels by regulating their RNA and protein levels, a phenomenon known as dosage compensation. However, the molecular mechanisms involved in dosage compensation in human cells - and whether they can be targeted to selectively kill aneuploid cancer cells - remain unknown. Here, we addressed this question via molecular dissection of multiple diploid vs. aneuploid cell models. Using genomic and functional profiling of a novel isogenic system of RPE1-hTERT cells with various degrees of aneuploidy, we found that aneuploid cells cope with both transcriptional burden and proteotoxic stress. At the mRNA level, aneuploid cells increased RNA synthesis, but concomitantly elevated several RNA degradation pathways, in particular the nonsense-mediated decay (NMD) and the microRNA-mediated mRNA silencing pathways. Consequently, aneuploid cells were more sensitive to the genetic or chemical perturbation of several key components of these RNA degradation pathways. At the protein level, aneuploid cells experienced proteotoxic stress, resulting in reduced translation and increased protein degradation, rendering them more sensitive to proteasome inhibition. These findings were recapitulated across hundreds of human cancer cell lines and primary tumors, confirming that both non-transformed and transformed cells alter their RNA and protein metabolism in order to adapt to the aneuploid state. Our results reveal that aneuploid cells are dependent on the over- or under-activation of several nodes along the gene expression process, identifying these pathways as clinically-actionable vulnerabilities of aneuploid cells.