Bayesian population reconstruction is a method for estimating past populations by age with fully probabilistic statements of uncertainty. It simultaneously estimates age-specific population counts, vital rates, and net migration from fragmentary data while formally accounting for measurement error. As inputs, it takes bias-reduced initial estimates of age-specific population counts, vital rates and net migration, and expert opinion about measurement error informed by data where available. We describe the new approach in the context of existing methods and demonstrate its flexibility by showing that it works well in countries with widely varying levels of data quality by applying it to very different countries, namely Laos and New Zealand. Remaining challenges and future directions will be discussed.