We concentrate on the rich effects that surface tension has on free and for
ced surface waves for Linear, nonlinear, and especially strongly nonlinear
waves close to or at breaking or their limiting form. These effects are dis
cussed in the context of standing gravity and gravity-capillary waves, Fara
day waves, and parasitic capillary waves. Focus is primarily on post-1989 r
esearch. Regarding standing waves, new waveforms and the large effect that
small capillarity can have are considered. Faraday waves are discussed prin
cipally with regard to viscous effects, hysteresis, and limit cycles; nonli
near waveforms of low mode numbers; contact-line effects and surfactants; b
reaking and subharmonics; and drop ejection. Pattern formation and chaotic
and nonlinear dynamics of Faraday waves are mentioned only briefly. Gravity
and gravity-capillary wave generation of parasitic capillaries and dissipa
tion are considered at length. We conclude with our view on the direction o
f future research in these areas.