In this talk we provide an overview of several forms of matrix structure (old and new) that arise in the context of fast recursive least-squares adaptive filtering, for both fixed-order and order-recursive implementations. While the literature has focused almost exclusively on fast filters for tapped-delay line implementations, we shall show that a more general theory exists that can accomodate more general filter structures. In the process we mention some open issues that are relevant for the development of truly reliable filter implementations, especially in quantized environments.