▪ Abstract  This review describes some of the important developments in the numerical investigation of transition to turbulence in wall-bounded and free shear flows during the past decade. The evolution of numerical techniques and models as well as the advances in our theoretical understanding of the physics of laminar-turbulent transition that were achieved using these tools are described. For wall-bounded flows, particular emphasis is placed on investigations studying various scenarios of “bypass transition” in flows that are asymptotically stable. A brief review of investigations into receptivity and control of transitional flows is included.