Although studies generally find evidence of a Phillips curve‐type relationship in South Africa, uncertainty remains about the relevance of the model over a relatively long sample period, and whether conventional output gap measures are suitable proxies for demand pressure. This paper reviews research which shows that the Phillips curve model prevails over an extended sample, provided that the benchmark specifications include major structural changes in the balance‐of‐payments and labour market, and account for shifts in the root causes of inflation. When this is done, a linear specification with an output gap in levels correctly predicts the non‐trended inflation pattern over the period 1971(Q1)–1984(Q4), whereas a piecewise concave curve with an output gap in growth rates accurately forecasts the decelerating inflation pattern during 1986(Q1)–2001(Q2). A novel feature of the concave model is that it remains statistically robust and structurally stable when it is estimated until 2015(Q4). The concave model imparts a disinflationary bias, which suggests that monetary policy should be more expansionary during downswing phases of the business cycle and neutral during upswing phases. The analysis also considers how the shape of the Phillips curve might change if the balance‐of‐payments constraint on demand is relaxed in a significant way.