Mangrove forests grow on saline, periodically flooded soils of the tropical and subtropical coasts. The tree species that comprise the mangrove are halophytes that have suites of traits that confer differing levels of tolerance of salinity, aridity, inundation and extremes of temperature. Here we review how climate change and elevated levels of atmospheric CO2 will influence mangrove forests. Tolerance of salinity and inundation in mangroves is associated with the efficient use of water for photosynthetic carbon gain which unpins anticipated gains in productivity with increasing levels of CO2. We review evidence of increases in productivity with increasing CO2, finding that enhancements in growth appear to be similar to trees in non-mangrove habitats and that gains in productivity with elevated CO2 are likely due to changes in biomass allocation. High levels of trait plasticity are observed in some mangrove species, which potentially facilitates their responses to climate change. Trait plasticity is associated with broad tolerance of salinity, aridity, low temperatures and nutrient availability. Because low temperatures and aridity place strong limits on mangrove growth at the edge of their current distribution, increasing temperatures over time and changing rainfall patterns are likely to have an important influence on the distribution of mangroves. We provide a global analysis based on plant traits and IPCC scenarios of changing temperature and aridity that indicates substantial global potential for mangrove expansion.