This paper deals with some of the features of static models of road traffic congestion that have caused much debate in the literature. It first focuses on the difficulties arising with the backward-bending cost curve defined over traffic flows in the context of 'continuous congestion'. The relevance of the backward-bending segment of this curve is questioned by demonstrating that the 'equilibria' on this segment of the cost curve are dynamically infeasible. Next, the implications for static models of 'peak congestion' are considered. In doing so, attention is paid also to 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 peak congestion.