Aging is characterized by a decline in various biological functions that is associated with changes in gene expression programs. Recent transcriptome-wide integrative studies in diverse organisms and tissues have revealed a gradual uncoupling between RNA and protein levels with aging, which highlights the importance of post-transcriptional regulatory processes. Here, we provide an overview of multi-omics analyses that show the progressive uncorrelation of transcriptomes and proteomes during the course of healthy aging. We then describe the molecular changes leading to global downregulation of protein synthesis with age and review recent work dissecting the mechanisms involved in gene-specific translational regulation in complementary model organisms. These mechanisms include the recognition of regulated mRNAs by trans-acting factors such as miRNA and RNA-binding proteins, the condensation of mRNAs into repressive cytoplasmic RNP granules, and the pausing of ribosomes at specific residues. Lastly, we mention future challenges of this emerging field, possible buffering functions as well as potential links with disease.