An integrable shock, or discontinuity, is a type of 'defect' allowed, in the sense of not destroying the property of integrability, within (at least some) integrable field theories. A main example is the sine-Gordon model, or, more generally, the a-series of affine Toda field theories. Such 'defects' have interesting properties in the classical and quantum domains especially with regard to their interactions with solitons - or indeed with each other, if there is more than one of them and they are allowed to move. This talk will present a survey of recent results and describe some open problems.