Climate change is expected to lead to more frequent, intense and longer droughts in the future, with major implications for ecosystem processes and human livelihoods. The impacts of such droughts are already evident, with vegetation dieback reported from a range of ecosystems, including savannas, in recent years.Most of our insights into the mechanisms governing vegetation drought responses have come from forests and temperate grasslands, while responses of savannas have received less attention. Because the two life forms that dominate savannas—C3 trees and C4 grasses—respond differently to the same environmental controls, savanna responses to droughts can differ from those of forests and grasslands.Drought‐driven mortality of savanna vegetation is not readily predicted by just plant drought‐tolerance traits alone, but is the net outcome of multiple factors, including drought‐avoidance strategies, landscape and neighborhood context, and impacts of past and current stressors including fire, herbivory and inter‐life form competition.Many savannas currently appear to have the capacity to recover from moderate to severe short‐term droughts, although recovery times can be substantial. Factors facilitating recovery include the resprouting ability of vegetation, enhanced flowering and seeding and post‐drought amelioration of herbivory and fire. Future increases in drought severity, length and frequency can interrupt recovery trajectories and lead to compositional shifts, and thus pose substantial threats, particularly to arid and semi‐arid savannas.Synthesis. Our understanding of, and ability to predict, savanna drought responses is currently limited by availability of relevant data, and there is an urgent need for campaigns quantifying drought‐survival traits across diverse savannas. Importantly, these campaigns must move beyond reliance on a limited set of plant functional traits to identifying suites of physiological, morphological, anatomical and structural traits or "syndromes" that encapsulate both avoidance and tolerance strategies. There is also a critical need for a global network of long‐term savanna monitoring sites as these can provide key insights into factors influencing both resistance and resilience of different savannas to droughts. Such efforts, coupled with site‐specific rainfall manipulation experiments that characterize plant trait–drought response relationships, and modelling efforts, will enable a more comprehensive understanding of savanna drought responses. [ABSTRACT FROM AUTHOR]