Aspects of defects in integrable quantum field theory

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.