Abstract: In this presentation we will look at Long Memory and Gegenbauer Long Memory processes, and methods for estimation of the parameters of these models. After a review of the history of the development of these processes, and some of the personalities involved, we will introduce a new method for the estimation of almost all the parameters of a k-factor Gegenbauer/GARMA process. The method essentially attempts to find parameters for the spectral density to ensure it most closely matches the (smoothed) periodogram. Simulations indicate that the new method has a similar level of accuracy to existing methods (Whittle, Conditional Sum-of-squares), but can be evaluated considerably faster, whilst making few distributional assumptions on the data.