Mitochondria have a central role in cellular metabolism; they are responsible for the biosynthesis of amino acids, lipids, iron–sulphur clusters and regulate apoptosis. About 99% of mitochondrial proteins are encoded by nuclear genes, so the biogenesis of mitochondria heavily depends on protein import pathways into the organelle. An intricate system of well-studied import machinery facilitates the import of mitochondrial proteins. In addition, folding of the newly synthesized proteins takes place in a busy environment. A system of folding helper proteins, molecular chaperones and co-chaperones, are present to maintain proper conformation and thus avoid protein aggregation and premature damage. The components of the import machinery are well characterised, but the targeting signals and how they are recognised and decoded remains in some cases unclear. Here we provide some detail on the types of targeting signals involved in the protein import process. Furthermore, we discuss the very elaborate chaperone systems of the intermembrane space that are needed to overcome the particular challenges for the folding process in this compartment. The mechanisms that sustain productive folding in the face of aggregation and damage in mitochondria are critical components of the stress response and play an important role in cell homeostasis.