Many biological surfaces in both the plant and animal kingdom possess unusual structural features at the micro- and nanometre-scale that control their interaction with water and hence wettability. An intriguing example is provided by desert beetles, which use micrometre-sized patterns of hydrophobic and hydrophilic regions on their backs to capture water from humid air. As anyone who has admired spider webs adorned with dew drops will appreciate, spider silk is also capable of efficiently collecting water from air. Here we show that the water-collecting ability of the capture silk of the cribellate spider Uloborus walckenaerius is the result of a unique fibre structure that forms after wetting, with the 'wet-rebuilt' fibres characterized by periodic spindle-knots made of random nanofibrils and separated by joints made of aligned nanofibrils. These structural features result in a surface energy gradient between the spindle-knots and the joints and also in a difference in Laplace pressure, with both factors acting together to achieve continuous condensation and directional collection of water drops around spindle-knots. Submillimetre-sized liquid drops have been driven by surface energy gradients or a difference in Laplace pressure, but until now neither force on its own has been used to overcome the larger hysteresis effects that make the movement of micrometre-sized drops more difficult. By tapping into both driving forces, spider silk achieves this task. Inspired by this finding, we designed artificial fibres that mimic the structural features of silk and exhibit its directional water-collecting ability.