Translation occurs primarily on ribosomes, the cellular machines that build proteins. In most cells, translation happens in the cytoplasm, after mRNA exits the nucleus (in eukaryotes) or directly in the cytosol (in prokaryotes). Ribosomes can be free-floating in the cytosol or attached to the endoplasmic reticulum in eukaryotic cells; in both cases, they read the mRNA sequence and synthesize the corresponding polypeptide. Key points:

• Location by organism:
  • Eukaryotes: translation occurs in the cytoplasm (and on rough ER for proteins destined for secretion or membranes).

* Prokaryotes: translation can begin while transcription is still ongoing in the cytosol, with ribosomes binding to nascent mRNA (no nucleus).

• Subcellular details:
  • The ribosome is the site of translation, composed of ribosomal RNA and proteins.

* In eukaryotes, mature mRNA must first be exported from the nucleus to the cytoplasm before translation; some proteins are targeted to the ER and then translated there via co-translational translocation.

• Special-case routing:
  • If a protein is intended for secretion or for membranes, translation may begin on free ribosomes and then continue on ribosomes attached to the rough ER, guiding the nascent protein into the secretory pathway.

If you want, I can pull up concise, up-to-date sources for a quick reading list or explain how translation is studied in the lab.