Understanding which species are able to recover from drought, under what conditions, and the mechanistic processes involved, will facilitate predictions of plant mortality in response to global change. In response to drought, some species die because of embolism-induced hydraulic failure, whilst others are able to avoid mortality and recover, following rehydration. Several tree species have evolved strategies to avoid embolism, whereas others tolerate high embolism rates but can recover their hydraulic functioning upon drought relief. Here, we focus on structures and processes that might allow some plants to recover from drought stress via embolism reversal. We provide insights into how embolism repair may have evolved, anatomical and physiological features that facilitate this process, and describe possible trade-offs and related costs. Recent controversies on methods used for estimating embolism formation/repair are also discussed, providing some methodological suggestions. Although controversial, embolism repair processes are apparently based on the activity of phloem and ray/axial parenchyma. The mechanism is energetically demanding, and the costs to plants include metabolism and transport of soluble sugars, water and inorganic ions. We propose that embolism repair should be considered as a possible component of a 'hydraulic efficiency-safety' spectrum. We also advance a framework for vegetation models, describing how vulnerability curves may change in hydrodynamic model formulations for plants that recover from embolism.