Digital try-on systems for e-commerce have the potential to change people's lives and provide notable economic benefits. However, their development is limited by practical constraints, such as accurate sizing of the body and realism of demonstrations. We enumerate three open challenges remaining for a complete and easy-to-use try-on system that recent advances in machine learning make increasingly tractable. For each, we describe the problem, introduce state-of-the-art approaches, and provide future directions.