The talk will be a review of some of the properties of defects that can be supported by at least some integrable field theories describing massive scalar particles, including the apparently central role played by energy and momentum stored by the defect. The sine-Gordon model is the simplest of these, and for this talk the main example, but there are many others. There are a number of open problems in both the classical and quantum field theory that will be described.

Though defects in a general sense are ubiquitous and much-studied within statistical mechanics models it is only recently that they have been considered within integrable field theory. At first sight, defects could be considered disastrous since the property of integrability might be lost. However, it turns out that not only is it possible to have 'integrable defects' but they have a range of interesting properties and cast some new light on traditional features. Several examples will be described, together with their properties in classical and quantum versions of the models.

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.