Modelling trends and cycles in economic time series has a long history, with the use of linear trends and moving averages forming the basic tool kit of economists until the 1970s. Several developments in econometrics then led to an overhaul of the techniques used to extract trends and cycles from time series. Terence Mills introduces these various approaches to allow students and researchers to appreciate the variety of techniques and the considerations that underpin their choice for modelling trends and cycles.