Recent advances in human genetics, together with a large body of epidemiologic, preclinical, and clinical trial results, provide strong support for a causal association between triglycerides (TG), TG-rich lipoproteins (TRL), and TRL remnants, and increased risk of myocardial infarction, ischaemic stroke, and aortic valve stenosis. These data also indicate that TRL and their remnants may contribute significantly to residual cardiovascular risk in patients on optimized low-density lipoprotein (LDL)-lowering therapy. This statement critically appraises current understanding of the structure, function, and metabolism of TRL, and their pathophysiological role in atherosclerotic cardiovascular disease (ASCVD). Key points are (i) a working definition of normo- and hypertriglyceridaemic states and their relation to risk of ASCVD, (ii) a conceptual framework for the generation of remnants due to dysregulation of TRL production, lipolysis, and remodelling, as well as clearance of remnant lipoproteins from the circulation, (iii) the pleiotropic proatherogenic actions of TRL and remnants at the arterial wall, (iv) challenges in defining, quantitating, and assessing the atherogenic properties of remnant particles, and (v) exploration of the relative atherogenicity of TRL and remnants compared to LDL. Assessment of these issues provides a foundation for evaluating approaches to effectively reduce levels of TRL and remnants by targeting either production, lipolysis, or hepatic clearance, or a combination of these mechanisms. This consensus statement updates current understanding in an integrated manner, thereby providing a platform for new therapeutic paradigms targeting TRL and their remnants, with the aim of reducing the risk of ASCVD.