Flow separation from lifting surfaces such as airfoils is undesirable as it deteriorates performance. For example, when airfoils that are designed for large Reynolds numbers are operated at smaller off-design Reynolds numbers, laminar separation can occur. Laminar separation typically leads to transition and reattachment. Transition is influenced by factors, such as free-stream turbulence and wall roughness. Transition and reattachment affect the circulation and, thereby, separation itself. We are employing computational fluid dynamics for investigating the fundamental mechanisms of separation and transition for lifting surfaces. Using highly-resolved direct numerical simulations, we are investigating fundamental aspects of separation and transition in the presence of free-stream turbulence for canonical separation bubbles. In parallel, we are carrying out hybrid turbulence model simulations of an entire airfoil at a larger chord Reynolds number. The combined approach will advance both physical understanding and modeling capabilities, and thus provide a solid platform for the development of separation control strategies for practical applications.