This chapter investigates the topic of orthographic reconstruction of a historical writing system taking as case study the Linear B syllabary of Bronze Age Greece. The Linear B syllabary was used to render the oldest Greek dialect attested in written form, so-called ‘Mycenaean’ Greek (c. 1400–1190 BC). The reader is guided step-by-step through the stages involved in the reconstruction of the orthography of the Linear B syllabary, so as to understand how to bridge the gap between actual attestations and their phonetic rendering (e.g. Linear B a-to-ro-qo representing alphabetic Greek ?????p?? /anthropos/ ‘man’). The discussion covers some of the methodological issues scholars had to reckon with when reconstructing a historical orthographic system in the Bronze Age Aegean context. This complex process eventually made it possible to draw up the ‘rules’ that govern the system and, by assessing deviations, to evaluate the extent to which these were adhered to. This chapter also illustrates the role played in such reconstruction by the historical and linguistic backdrop, within which the adaptation of an already existing writing system (‘Minoan’ Linear A) took place to render a linguistically different language (Greek).