Ice sheet mass balance (and therefore sea-level contribution) is buttressed at its margins by the ice shelves. Across Antarctica, the stability of these ice shelves, on which this buttressing effect depends, is known to be compromised by ocean-driven basal melting and iceberg calving. However, recent discoveries of widespread and persistent surface meltwater drainage systems (on grounded and floating ice) have been hypothesised to exert an increasingly prevalent destabilising effect on Antarctic ice shelves. In this critical review, the feedback mechanisms by which meltwater lakes and channels affect the ice-shelf surface and structural properties are examined. Drawing on these and analysis of circum-Antarctic observations, it becomes apparent that surface meltwater is indeed likely to have destabilising effect on most Antarctic ice shelves. This is largely due to their topography and growing meltwater budget as the climate warms. This is supported by further evidence from observations of wintertime melt and basal-induced concentrated thinning, which should initiate even greater instability. However, models are yet to include these effects, or accurately simulate surface water flow on ice shelves. Therefore, surface meltwater is likely to destabilise Antarctic ice shelves to a greater extent than current models can forecast.