This paper studies some of the properties and fundamentals of static models of road traffic congestion that have triggered much debate in the literature. The first part of the paper focuses in particular on the difficulties arising with the backward-bending cost curve in the context of 'continuous congestion'. Therelevance of the backward-bending segment of the cost curve for the static analysis of congestion is questioned by demonstrating that 'equilibria' on this segment produce upwards shifts of the cost curve itself, and can therefore not be of a stationary nature. Next, the implications for static models of 'peakcongestion' are considered. In doing so, the paper addresses the implicit assumptions, particularly on the nature of scheduling costs, that are necessary to render static models of peak congestion internally consistent. The paper ends with a brief discussion of the implications for dynamic models of peakcongestion.