  Defects are ubiquitous in nature, for example dislocations, shocks, bores, or
impurities of various kinds, and their descriptions are an important part of
any physical theory. However, one might ask the question: what types of defect
are allowed and what are their properties if it is required to maintain
integrability within an integrable field theory in two-dimensional space-time?
This talk addresses a collection of ideas and questions including examples of
integrable defects and the curiously special roles played by energy-momentum
conservation and Backlund transformations, solitons scattering with defects and
some interesting effects within the sine-Gordon model, defects in integrable
quantum field theory and the construction of transmission matrices, and
concluding with remarks on algebraic considerations and future directions.
