Mitochondria are involved in several vital functions of the eukaryotic cell. The majority of mitochondrial proteins are coded by nuclear DNA. Constant import of proteins from the cytosol is a prerequisite for the efficient functioning of the organelle. The protein import into mitochondria is mediated by diverse import pathways and is continuously under watch by quality control systems. However, it is often challenged by both internal and external factors, such as oxidative stress or energy shortage. The impaired protein import and biogenesis leads to the accumulation of mitochondrial precursor proteins in the cytosol and activates several stress response pathways. These defense mechanisms engage a network of processes involving transcription, translation, and protein clearance to restore cellular protein homeostasis. In this review, we provide a comprehensive analysis of various factors and processes contributing to mitochondrial stress caused by protein biogenesis failure and summarize the recovery mechanisms employed by the cell.