The poor can and do save, but often use formal or informal instruments that have high risk, high cost, and sub-optimal design. This could lead to undersaving compared to a world without market or behavioral frictions. Undersaving has important welfare consequences: variable consumption, low resilience to shocks, and foregone profitable investments. We lay out five sets of constraints that may hinder the adoption and effective usage of savings products and services by the poor: transaction costs, lack of trust and regulatory barriers, information and knowledge gaps, social constraints and behavioral biases. We discuss each in theory, and then summarize related empirical evidence, with a focus on recent field experiments. We then put forward key open areas for research and practice.