Wormlike micelle (WLM)-forming surfactants are common ingredients in consumer products such as shampoos, detergents, and cosmetics; industrial fluids used in applications such as inkjet printing, enhanced oil recovery and turbulent drag reduction; and biomedical applications such as drug delivery and biosensors. Many of these applications involve flow of WLM solutions through complex geometries with a range of characteristic length-scales that can reach down to the microscale. Despite their extensive use, there are still many details that are not clearly understood about the microscopic micellar structure and the mechanisms by which WLMs form and deform under flow. Microfluidic devices provide a versatile platform to study WLM solutions under various flow conditions and in confined geometries that can be simplified and idealized, or that can be made to mimic conditions found in applications. Here we present a review of recent investigations using microfluidics to study the flow of WLMs, with an emphasis on three different flow types: shear, elongation, and complex mixed flow fields. In particular, we focus on the use of shear flows to study shear banding and assess the steady shear rheology; the use of extension-dominated flows (both stagnation point and transient) to assess the elongational viscosity and study elastic instabilities of wormlike micellar solutions. Finally, we discuss the use of complex flow fields incorporating combinations of strong shearing and extensional deformations in confined microfluidic geometries in order to generate a stable and nanoporous flow-induced structured phase (FISP) from WLM solutions. The FISP has potential applications in encapsulation of molecules, functionalized nanostructured materials, and for environmental sensing. This review shows that the influence of spatial confinement and hydrodynamic forces present in microfluidic devices can give rise to a range of interesting flow phenomena intimitely related to microstructural rearrangements of wormlike micelles in solution.