Due to their inherent nonlinearity, the vast majority of solutions for shear flows have been discovered only in the last 10-15 years. These solutions take the form of a travelling wave (TW). Their discovery has permitted a new theoretical framework, where the TWs and their unstable eigenvectors form a skeleton in phase space for the trajectories taken by a chaotic turbulent flow. At large Reynolds numbers, application of this approach is increasingly difficult, since the number of degrees of freedom increases as the turbulent eddies become small. Meanwhile, however, in experiments at very large Reynolds numbers, mostly in pipe flow, it is the discovery of large scale motions (LSMs) and very large scale motions (VLSMs) that has attracted interest over the last decade. In this talk we first review the progress in connecting turbulent dynamics with travelling waves and periodic orbits in pipe flow. Then, by parameterising the effect of the smallest eddies (via LES simulation), we seek nonlinear solutions that may help us understand the origin and dynamics of the LSMs and VLSMs.