This thesis focuses on numerical studies of subcritical transition to turbulence in shear flows. The thesis employs a framework based on nonlinear dynamics in the subsequent studies. The geometrical approach to subcritical transition pivots the concepts of edge manifold and edge state. Such concepts are explored in detail in the Blasius boundary layer. The identified edge trajectory is chaotic and presents a couple of high- and low-speed streaks akin to those identified in other shear flows. For long enough times the linear instability of the Blasiusboundary layer coexists with the bypass transition scenario. The edge is thus reinterpreted as a manifold separating both routes. On the edge manifold of the Blasius boundary layer, the fully localised minimal seed is identified. The minimal seed experiences a sequence of linear mechanisms: the Orr mechanism followed by the lift-up. The resulting perturbation approaches the same region in state space as identified from arbitrary perturbations.These insights from the edge trajectory identified in the Blasius boundary layer inspired a low-dimensional model. The model illustrates the e↵ect of the laminar attractor becoming linearly unstable and it agrees qualitatively withother recent studies in the literature.The edge has been identified as a hyperbolic Lagrangian coherent structure of infinite dimension. We show how two Lagrangian diagnostics can be used to locate the edge directly in state space. This allows us to revisit edge tracking as a method optimising a Lagrangian diagnostic instead of a binary algorithm.The two last studies of the thesis focus on the optimally time-dependent(OTD) modes as a basis for the linearised dynamics about a base flow with arbitrary time-dependence. The OTD modes are explored for a periodic flow in pulsating plane Poiseuille flow. The resulting OTD modes can be linked to thespectrum of the Orr-Sommerfeld operator. The results revealed perturbations which span more than one period of the base flow. Finally, the OTD frameworkis used on the edge trajectory starting from the minimal seed in the Blasiusboundary layer.