Maintaining laminar flow and delaying transition to turbulence on aircraft wings reduces friction drag and hence fuel consumption for an improved ecological footprint. Nonetheless, widespread models of disturbance growth in boundary layers discard important transition stages and are inadequate to incorporate the effect of surface irregularities causing rapid variations in the underlying steady flow. This thesis applies global or Harmonic Navier-Stokes (HNS) methods to quantify the growth of instabilities in shear flows with two inhomogeneous spatial directions. Such methods deliver greater fidelity than the standard Parabolised Stability Equations (PSE). This work presents an efficient parallel computational framework to solve linear and non-linear HNS problems. We use BiGlobal analysis to investigate the existence of temporally unstable modes on a flat plate with smooth indentations featuring laminar separation bubbles (LSBs). Then, for the first time, it is applied to a swept-wing boundary layer featuring Backward- and Forward-Facing Steps (BFSs and FFSs). Localised unstable modes are identified for step heights exceeding the local boundary-layer displacement thickness of the clean geometry. BFSs are found to be more destabilising than equivalent FFSs, especially in the presence of the LSB formed behind the infinite-swept BFS. Next, we introduce the non-linear HNS method as an improvement over the non-linear PSE, able to model receptivity and non-linear mode interaction at a fraction of the cost of Direct Numerical Simulation. The method can model flow destabilisation scenarios on swept wings exhibiting surface features and holds the potential for accurate transition prediction. Its performance is assessed in the case of a Tollmien-Schlichting wave interacting with a cylindrical roughness located on a nearly flat aerofoil section. Finally, we consider crossflow disturbances generated by placing Discrete Roughness Elements (DRE) at the leading edge of a swept wing and follow their non-linear development up to a strongly saturated state. Non-linear receptivity effects are found to arise with increasing DRE heights.