Bypass transition in flat-plate boundary layers due to a highly disturbed free stream is investigated via numerical simulation. The first part of the study presents DNS & LES of the interaction between a laminar boundary layer and a von Karman vortex street behind a circular cylinder. Rapid, bypass-like transition to turbulence is observed for higher Reynolds number cases. An investigation of the underlying transition mechanism is performed. The second part of the study focuses on transition due to the effects of isotropic free-stream turbulence (FST). First, the effects of different inflow parameters on the location of transition onset are examined. The length scale of the FST and the extent of its penetration into the boundary layer are among the parameters that affect srongly the transition onset location. In subsequent simulations, we include the leading edge of the flat plate inside the computational domain. The results reveal the presence of small-amplitude laminar streaks at the streamwise location corresponding to the inflow boundary of the truncated-domain simulations. We conclude that such simulations should not be expected to provide quantitative predictions of bypass transition. However, with suitable calibration, they represent a useful tool for investigating bypass transition physics. Finally, DNS of bypass transition in the flat-plate boundary layer induced by high-amplitude FST are carried out. In one simulation, the boundary conditions are chosen to match the 6% FST ERCOFTAC experiment T3B. The mean velocity and Reynolds stress profiles are in good agreement with the experimental dataset. In the other simulations, the length scale and intensity of the oncoming FST are varied to determine the effects on the onset and mechanism of transition. Our results indicate that the physics of FST-induced boundary-layer transition are dependent on the choice of the FST length scale. A description of statistical quantities is followed by a study of the transition mechanism. Qualitative similarities between bypass transition due to FST and wake-induced transition are underlined and the challenges of predicting boundary-layer transition in this complex environment are discussed.