Asymmetric unilamellar vesicles are aqueous bodies surrounded by two dissimilar leaflets made from lipids, polymers, or both. They are great models for cell membranes and attractive vehicles in potential biomedicine applications. Despite their promise, asymmetric unilamellar vesicles are not widely studied or adopted in applications. This is largely due to the complexity in generating asymmetric membranes. Recent technical advances in microfluidics have opened doors to high throughput fabrication of asymmetric unilamellar vesicles. In this review, we focus on microfluidic methods for generating asymmetric lipid vesicles, with two dissimilar lipid leaflets, and asymmetric lipid-polymer vesicles, with one lipid leaflet and one polymer leaflet. We also review a few standard non-microfluidic methods for generating asymmetric vesicles. We hope to highlight the improved capability in obtaining asymmetric vesicles through a variety of methods and encourage the wider scientific community to adopt some of these for their own work.