Regression with a circular response is a topic of current interest. We introduce non-parametric smoothing for this problem. Simple adaptations of a weight function enable a unified formulation for both real-line and circular predictors, whereas these cases have been tackled by quite distinct parametric methods. Additionally, we discuss various methodological extensions, obtaining a number of promising techniques – totally new in circular statistics – such as confidence intervals for the value of a circular regression and non-parametric autoregression in circular time series. The findings are also illustrated through real data examples.