Over the last few decades, increasing attention has been paid to understanding the pathophysiology, aetiology, prognosis, and treatment of elevated intra-abdominal pressure (IAP) in trauma, surgical, and medical patients. However, there is presently a relatively poor understanding of intra-abdominal volume (IAV) and the relationship between IAV and IAP (i.e. abdominal compliance). Consensus definitions on Cab were discussed during the 5th World Congress on Abdominal Compartment Syndrome and a writing committee was formed to develop this article. During the writing process, a systematic and structured Medline and PubMed search was conducted to identify relevant studies relating to the topic. According to the recently updated consensus definitions of the World Society on Abdominal Compartment Syndrome (WSACS), abdominal compliance (Cab) is defined as a measure of the ease of abdominal expansion, which is determined by the elasticity of the abdominal wall and diaphragm. It should be expressed as the change in IAV per change in IAP (mL [mm Hg]-1). Importantly, Cab is measured differently than IAP and the abdominal wall (and its compliance) is only a part of the total abdominal pressure-volume (PV) relationship. During an increase in IAV, different phases are encountered: the reshaping, stretching, and pressurisation phases. The first part of this review article starts with a comprehensive list of the different definitions related to IAP (at baseline, during respiratory variations, at maximal IAV), IAV (at baseline, additional volume, abdominal workspace, maximal and unadapted volume), and abdominal compliance and elastance (i.e. the relationship between IAV and IAP). An historical background on the pathophysiology related to IAP, IAV and Cab follows this. Measurement of Cab is difficult at the bedside and can only be done in a case of change (removal or addition) in IAV. The Cab is one of the most neglected parameters in critically ill patients, although it plays a key role in understanding the deleterious effects of unadapted IAV on IAP and end-organ perfusion. The definitions presented herein will help to understand the key mechanisms in relation to Cab and clinical conditions and should be used for future clinical and basic science research. Specific measurement methods, guidelines and recommendations for clinical management of patients with low Cab are published in a separate review.