Purpose. Postural control during quiet standing has been modeled by concepts using kinematic variables estimated from center of pressure (COP) signals. The concept of position-based postural control has had particular ramifications in the literature, although a more recent concept of velocity-based control has been proposed as being more relevant. Methods. This study reviews the literature investigating these concepts and their respective quantitative methods alongside current supporting evidence and criticisms. Results. The position-based control concept suggests the existence of two control loops that alternate whenever certain thresholds are exceeded. Such a theory is supported by studies describing the time delay between the skeletal muscle activation and CoP displacement. However, this concept has been criticized to be the result of statistical artifacts due to it not being adapted to the analysis of bounded time series. Conversely, the velocity-based control concept claims that velocity is the most relevant kinematic variable for postural control. Such a theory suggests that postural adjustments are executed to change the trajectory of the CoP whenever the velocity crosses a threshold. Both theories have their major methodological limitations, while interpretation of data from the position-based concept is difficult, velocity-based thresholds are empirical and still need verification in different motor tasks and populations. Conclusions. Given the observed similarities and mutual exclusivity of both concepts, there is a need for the development of methods that can quantitatively analyze stabilometric signals while simultaneously considering both kinematic variables.