While force-velocity-power characteristics of resistance exercises, such as bench presses and squats, have been well documented, little attention has been paid to load, force, and power-velocity relationships in exercises engaging core muscles. Given that power produced during lifting tasks or trunk rotations plays an important role in most sport-specific and daily life activities, its measurement should represent an important part of the test battery in both athletes and the general population. The aim of this scoping review was 1) to map the literature related to testing methods assessing core muscle strength and stability in sport and rehabilitation, chiefly studies with particular focus on force-velocity-power characteristics of exercises involving the use of core muscles, 2) and to identify gaps in existing studies and suggest further research in this field. The literature search was conducted on Cochrane Library databases, Scopus, Web of Science, PubMed and MEDLINE, which was completed by SpringerLink, Google Scholar and Elsevier. The inclusion criteria were met in 37 articles. Results revealed that among a variety of studies investigating the core stability and core strength in sport and rehabilitation, only few of them analyzed force–velocity–power characteristics of exercises involving the use of core muscles. Most of them evaluated maximal isometric strength of the core and its endurance. However, there are some studies that assessed muscle power during lifting tasks at different loads performed either with free weights or using the Smith machine. Similarly, power and velocity were assessed during trunk rotations performed with different weights when standing or sitting. Nevertheless, there is still scant research investigating the power-velocity and force-velocity relationship during exercises engaging core muscles in able-bodied and para athletes with different demands on stability and strength of the core. Therefore, more research is needed to address this gap in the literature and aim research at assessing strength and power-related measures within cross-sectional and intervention studies. A better understanding of the power-force-velocity profiles during exercises with high demands on the core musculature has implications for designing sport training and rehabilitation programs for enhancement of athletes’ performance and/or decrease their risk of back pain.