MultiJEDI (Multilingual Joint Word Sense Disambiguation) is a 5-year research program that investigates radically new directions for performing multilingual WSD. The key intuition underlying the project is that WSD can be performed globally to exploit at the same time knowledge available in many languages. The first stage of the project involved the development of a methodology for automatically creating a large-scale, multilingual knowledge base: BabelNet (http://babelnet.org). In a second stage, using this lexical resource, novel graph-based algorithms for jointly performing disambiguation across different languages have been designed and experimented, including Babelfy (http://babelfy.org). Overall, the project has two main objectives: creating large-scale lexical resources for dozens of languages, and enabling multilingual text understanding. Crucially, we show that these two tasks are mutually beneficial for going beyond current state-of-the-art WSD systems. Ongoing research within the MULTIJEDI project not only has impact on WSD research, but also on related areas such as Information Retrieval and Machine Translation.