Mammalian mitochondrial ribosomes (mitoribosomes) synthesize a small subset of proteins, which are essential components of the oxidative phosphorylation machinery. Therefore, their function is of fundamental importance to cellular metabolism. The assembly of mitoribosomes is a complex process that progresses through numerous maturation and protein-binding events coordinated by the actions of several assembly factors. Dysregulation of mitoribosome production is increasingly recognized as a contributor to metabolic and neurodegenerative diseases. In recent years, mutations in multiple components of the mitoribosome assembly machinery have been associated with a range of human pathologies, highlighting their importance to cell function and health. Here, we provide a review of our current understanding of mitoribosome biogenesis, highlighting the key factors involved in this process and the growing number of mutations in genes encoding mitoribosomal RNAs, proteins, and assembly factors that lead to human disease.