Proceedings of the Particle Physics and Early Universe Conference (PPEUC). For this paper: postscript PPEUC CMB index 1 Introduction.. ... We review recent work on a new class of topological defects which possess a non-symmetric core. They arise in scalar field theories with global symmetries, for domain walls and for vortices, which are explicitly broken to and respectively. ... 2 Domain Walls with Non-Symmetric Cores . 3 Vortices with Non-symmetric Core . ... PPEUC Proceedings . ...