In turbulent flows at low Reynolds numbers localized structures are observed which can grow or spontaneously decay. Viewed as a dynamical system, a turbulent evolution forms a path through a phase space built upon exact invariant solutions of the Navier-Stokes equations. The leading stable and unstable manifolds of these solutions organise the local dynamics. In small periodic domains many of these solutions are known. However, to understand the full spatial-temporal nature of turbulence requires localized solutions which are unstable and live in a very high dimensional system. In the first half of this thesis we consider two problems in small, periodic domains where turbulence is global. We consider the geometry of the edge of chaos, a manifold which divides phase space and how such a manifold can be understood in the context of turbulent decay. We demonstrate that the edge is not separate from the turbulent dynamics but is wrapped up into these dynamics. Next we consider how the dynamics on the edge in short pipes are affected by Reynolds number and find new high Reynolds number solutions. In this second half we attack the problem of finding and understanding the origins of localized solutions. These solutions hold the key to expanding the theory towards physically realisable systems. Building upon the short pipe research we find the origin of the first localized pipe flow solution in a bifurcation from a downstream-periodic solution. Moving to a model for plane Couette flow, we attempt to find evidence of homoclinic-snaking as a route to spanwise localization. Instead we find a different route which matches recent work in duct flow. Finally, motivated by questions of how localized structures interact, we introduce a new flow, "localized Couette flow", and investigate the stability of this flow.