In this paper, we present the computational semantic lexicon of Modern Greek that has been built in the framework of the LE-SIMPLE project and is currently being extended in the LEXIS project. The LE-SIMPLE project, in which the model and basic features of the lexicon have been designed and implemented, aimed at the construction of harmonised semantic lexicons for Human Language Technology (HLT) applications in 12 European languages. The paper focuses on the model, which caters for the encoding of a large variety of semantic information, including ontological typing, argument structure and domain categorisation, and on its implementation for Modern Greek.