Well radius of influence and well radius of investigation are fundamental concepts in well hydraulics and well testing. However, a large confusion surrounds these concepts. Well radius of influence is loosely defined as the distance from the well at which the hydraulic head change induced by pumping (or injection) is negligible. Well radius of investigation is a closely related but different concept. Well radius of investigation is loosely defined as the distance from the well at which the aquifer properties have a negligible influence on the hydraulic head change at the well. In either case, several interpretations are possible of what may be considered as being a negligible hydraulic head change. Accordingly, various formulae have previously been proposed to estimate well radius of influence and well radius of investigation. These formulae can yield significant differences in the calculated values. However, there is no guidance as to when to use one formula rather than another. In this contribution, we present a critical review of available formulae and derive new formulae to overcome limitations of available ones. The formulae are classified into three categories: (i) formulae that are based on an absolute criterion, (ii) formulae that are based on a relative criterion, and (iii) heuristic formulae. This classification alleviates the confusion that surrounds the concepts of well radius of influence and well radius of investigation, and it highlights that different formulae may be best suited for different purposes. As an outcome, we propose a practical guide for choosing a suitable formula for well radius of influence and well radius of investigation according to the context of use.