The Voynich manuscript is a medieval text that has so far resisted all attempts of decipherment. It is often referred as the "most mysterious manuscript" and is considered a cryptographic and linguistic enigma. Its vellum has been dated to the second half of the 15th century, but apart from that, its origin, purpose, and meaning, still remain unknown. Here we overview some recent statistical evidence and present new findings supporting the hypothesis that the Voynich manuscript contains a genuine linguistic structure. We describe novel approaches to the problem of the Voynich manuscript using methods from information theory and statistics that quantify global patterns in the distribution of words. These methods allow the extraction of putative semantic networks between the most informative words. We also present recent evidence coming from the scaling properties of word frequencies and correlations that points towards an underlying structure compatible with natural languages. Finally, we discuss possible new research pathways that could be followed to shed some light on the mystery of the Voynich Manuscript.