Aberrant, misfolded, and mislocalized proteins are often toxic to cells and result in many human diseases. All proteins and their mRNA templates are subject to quality control. There are several distinct mechanisms that control the quality of mRNAs and proteins during translation at the ribosome. mRNA quality control systems, nonsense-mediated decay, non-stop decay, and no-go decay detect premature stop codons, the absence of a natural stop codon, and stalled ribosomes in translation, respectively, and degrade their mRNAs. Defective truncated polypeptide nascent chains generated from faulty mRNAs are degraded by ribosome-associated protein quality control pathways. Regulation of aberrant protein production, a novel pathway, senses aberrant proteins by monitoring the status of nascent chain interactions during translation and triggers degradation of their mRNA. Here, we review the current progress in understanding of the molecular mechanisms of mRNA and protein quality controls at the ribosome during translation.