•We provide a unique summary of the quantitative literature on the effects of density, providing recommended density elasticities for 15 distinct outcomes and novel insights into heterogeneity.•The density elasticity of wages, at 0.08, is twice as large for developing countries than for developed countries.•The density elasticity of rents is about 0.15 for US cities and increases by 0.063 for every increase in population density by 1000 inhabitants per square kilometre.•We provide novel estimates of the density elasticity of construction costs which ranges from 0.04 to 0.07.•Based on a world-wide sample of cities, we provide an estimate of the elasticity of density with respect to population size at 0.43. This paper synthesises the state of knowledge on the economic effects of density. We consider 347 estimates of density elasticities of a broad range of outcomes ranging from wages, innovation, rents, various amenities, the cost of providing public services, transport- and environment-related outcomes to health and wellbeing. More than 100 of these estimates have not been previously published and have been provided by authors on request or inferred from published results in auxiliary analyses. We contribute original estimates of density elasticities of 16 distinct outcome variables that belong to categories where the evidence base is thin, inconsistent or non-existent. Along with a critical discussion of the quality and the quantity of the evidence base we present a set of recommended elasticities. Applying them to a scenario that roughly corresponds to an average high-income city, we find that density seems to be a net-amenity that is associated with positive external welfare effects. Densification policies may be welfare enhancing, but the distributional effects may be regressive, especially if residents are immobile and housing supply is inelastic.