Abstract: This review describes someof the important developments in the numerical investigation oftransition to turbulence in wall-bounded and free shear flows during thepast decade. The evolution of numerical techniques and models as wellas the advances in our theoretical understanding of the physics oflaminar-turbulent transition that were achieved using these tools aredescribed. For wall-bounded flows, particular emphasis is placed oninvestigations studying various scenarios of ``bypass transition'' inflows that are asymptotically stable. A brief review of investigationsinto receptivity and control of transitional flows is included.