We investigate whether a class of trend models with various error term structures can improve upon the forecast performance of commonly used time series models when forecasting CPI inflation in Australia. The main result is that trend models tend to provide more accurate point and density forecasts compared to conventional autoregressive and Phillips curve models. The best short-term forecasts come from a trend model with stochastic volatility in the transitory component, while medium to long-run forecasts are better made by specifying a moving average component. We also find that trend models can capture various dynamics in periods of significance which conventional models cannot. This includes the dramatic reduction in inflation when the RBA adopted inflation targeting, the one-off 10 per cent Goods and Services Tax inflationary episode in 2000, and the gradual decline in inflation since 2014.