The mitochondrial ribosome (mitoribosome) is a multicomponent machine that has unique structural features. Biogenesis of the human mitoribosome includes correct maturation and folding of the mitochondria-encoded RNA components (12S and 16S mt-rRNAs, and mt-tRNAVal) and their assembly together with 82 nucleus-encoded mitoribosomal proteins. This complex process requires the coordinated action of multiple assembly factors. Recent advances in single-particle cryo-electron microscopy (cryo-EM) have provided detailed insights into the specific functions of several mitoribosome assembly factors and have defined their timing. In this review we summarize mitoribosomal small (mtSSU) and large subunit (mtLSU) biogenesis based on structural findings, and we discuss potential crosstalk between mtSSU and mtLSU assembly pathways as well as coordination between mitoribosome biogenesis and other processes involved in mitochondrial gene expression.