Toward the integrated synthesis and processing of functional block copolymer nanostructures, the physics of flow-induced alignment of block copolymers must be understood to predict the direction, rate and degree of alignment. In this review we focus on key issues regarding flow-induced alignment of lamellae. A three-dimensional mapping summarizes previous results on the selection of alignment directions (parallel or perpendicular) and their pathways in terms of three dimensionless parameters : frequency, temperature and strain amplitude. Trajectories, kinetics and structural evolution are explored in a fourth dimension (time). The challenge of developing adequate experimental methods for monitoring transient structure is discussed. A comprehensive experimental approach, which combines in-situ rheo-optical measurements and ex-situ structural characterization by electron microscopy and X-ray scattering, is presented as a new tool for tracking changes of microstructure and orientation during flow-induced alignment. Various mechanisms that have been proposed over the past two decades are reviewed and re-evaluated based on recent experimental results. Outstanding questions and new issues raised by ABC triblock copolymer nanstructures are discussed.