This review is devoted to open strings, and in particular to the often surprising features of their spectra. It follows and summarizes developments that took place mainly at the University of Rome “Tor Vergata” over the last decade, and centred on world-sheet aspects of the constructions now commonly referred to as “orientifolds”. Our presentation aims to bridge the gap between the world-sheet analysis, that first exhibited many of the novel features of these systems, and their geometric description in terms of extended objects, D-branes and O-planes, contributed by many other colleagues, and most notably by J. Polchinski. We therefore proceed through a number of prototype examples, starting from the bosonic string and moving on to ten-dimensional fermionic strings and their toroidal and orbifold compactifications, in an attempt to guide the reader in a self-contained journey to the more recent developments related to the breaking of supersymmetry.

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Carlo Angelantonj (CERN / Augusto Sagnotti (Pisa, Scuola Normale Superiore & INFN, Pisa) ©2016