In order to efficiently replicate, viruses require precise interactions with host components and often hijack the host cellular machinery for their own benefit. Several mechanisms involved in protein synthesis and processing are strongly affected and manipulated by viral infections. A better understanding of the interplay between viruses and their host-cell machinery will likely contribute to the development of novel antiviral strategies. Here, we discuss the current knowledge on the interactions between influenza A virus (IAV), the causative agent for most of the annual respiratory epidemics in humans, and the host cellular proteostasis machinery during infection. We focus on the manipulative capacity of this virus to usurp the cellular protein processing mechanisms and further review the protein quality control mechanisms in the cytosol and in the endoplasmic reticulum that are affected by this virus.