We present our demonstration of two machine translation applications to historical documents. The first task consists in generating a new version of a historical document, written in the modern version of its original language. The second application is limited to a document's orthography. It adapts the document's spelling to modern standards in order to achieve an orthography consistency and accounting for the lack of spelling conventions. We followed an interactive, adaptive framework that allows the user to introduce corrections to the system's hypothesis. The system reacts to these corrections by generating a new hypothesis that takes them into account. Once the user is satisfied with the system's hypothesis and validates it, the system adapts its model following an online learning strategy. This system is implemented following a client-server architecture. We developed a website which communicates with the neural models. All code is open-source and publicly available. The demonstration is hosted at http://demosmt.prhlt.upv.es/mthd/.