This thesis suggests a general approach for estimating the trend of a univariate time series. It begins by suggesting and defining a set of "desirable" trend properties, namely "Fidelity", "Smoothness", "Invariance" and "Additivity", which are then incorporated into the design of an appropriate non-stationary time series model. The unknown parameters of the model are then estimated using a wide selection of "optimal" procedures, each parameter having at least two such procedures applied to it. Attention is paid to the development of algorithms to implement the procedures in practice. The model is gradually extended from a basic, non-seasonal model consisting of a simple lagged trend to a general, seasonal model incorporating a variable parameter, general autoregressive trend.