Protein synthesis from mRNA is an energy-intensive and tightly controlled cellular process. Translation elongation is a well-coordinated, multifactorial step in translation that undergoes dynamic regulation owing to cellular state and environmental determinants. Recent studies involving genome-wide approaches have uncovered some crucial aspects of translation elongation including the mRNA itself and the nascent polypeptide chain. Additionally, these studies have fuelled quantitative and mathematical modelling of translation elongation. In this review, we provide a comprehensive overview of the key determinants of translation elongation. We discuss consequences of ribosome stalling or collision, and how the cells regulate translation in case of such events. Next, we review theoretical approaches and widely used mathematical models that have become an essential ingredient to interpret complex molecular datasets and study translation dynamics quantitatively. Finally, we review recent advances in live-cell reporter and related analysis techniques, to monitor the translation dynamics of single cells and single-mRNA molecules in real time.