In the present thesis, receptivity, stability and laminar-turbulent transition of different boundary-layer flows are addressed and investigated by means of direct numerical simulations. In particular, flows over a wing and a low-pressure-turbine (LPT) blade have been the main focus. Transition in a swept-wing boundary layer in the presence of free-stream turbulence (FST) and a disk-shaped roughness element is studied. In particular, for the subcritical roughness heights, the absence of FST leads to a stationary laminar flow, while the small amount of FST typical of a low-noise wind tunnel will cause the formation of turbulence spots. When FST intensity is increased by one order of magnitude, the wake is found to transition to turbulent in the vicinity of the roughness element. We show that the level of FST have a significant impact on the stability of the wake behind the roughness, which can explain some experimental observations. Moreover, the interaction of Tollmien-Schlichting waves with a cylindrical roughness element is considered. The results of such interaction is reported for the roughness heights which have not been covered previously in the literature. The effect of initial amplitude and different frequency has been analyzed. Using the energy budget analysis, we show that the main contribution to the growth of the waves is associated with the wall-normal gradient of the streamwise velocity. A major part of the thesis concerns the laminar-turbulent transition process over a low-pressure-turbine blade. Here, two different levels of FST are considered. In the low FST intensity, the boundary layer over the suction side of the LPT blade starts to separate close to the trailing edge leading to the formation of quasi-two-dimensional Kelvin-Helmholtz vortices. At the high levels of FST, the flow separation is suppressed, and the transition is caused by the breakup of the streaks generated inside the boundary layer. The numerical results are found to agree well with those from the reference experiment. Different modal-decomposition techniques are used to study the receptivity of the blade boundary layer to the external disturbances in the case of high FST. Especially, the roles of the leading-edge receptivity and the continuous forcing by the FST in the blade passage has been investigated. The growth of the disturbances highlighted by the modal decomposition is compared with the one predicted by the optimal disturbance analysis. The work shows that the influence of the FST in the blade passage plays a central role in the development of the disturbances, which leads to transition on the suction side. Further, the effects of the wakes shed by the upstream turbine blades on the transition is studied. Here, the upstream blades are modelled by moving bars. It is found that the suction side of the blade is mainly affected by the presence of the wakes and the dominant frequency inside the boundary layer corresponds to that of the passing bars. The boundary-layer profiles exhibit higher mean velocities close to the surface resulting in higher values of the shear stress compared to the case without the moving bars, especially in the rear part of the blade. Moreover, high values of the velocity perturbations are observed inside the boundary layer and their amplitude changes during a period depending on the location of the wakes relative to the leading edge.