Even in simple geometries, many complex fluids display nontrivial flow fields, with regions where shear is concentrated. The possibility for such shear banding has been known for several decades, but in recent years, we have seen an upsurge in studies offering an ever-more precise understanding of the phenomenon. The development of new techniques to probe the flow on multiple scales with increasing spatial and temporal resolution has opened the possibility for a synthesis of the many phenomena that could only have been thought of separately before. In this review, we bring together recent research on shear banding in polymeric and soft glassy materials and highlight their similarities and disparities.