Organizations like the Internet Archive have been capturing Web contents over decades, building up huge repositories of time-versioned pages. The timestamp annotations and the sheer volume of multi-modal content constitutes a gold mine for analysts of all sorts, across diff�erent application areas, from political analysts and marketing agencies to academic researchers and product developers. In contrast to traditional data analytics on click logs, the focus is on longitudinal studies over very long horizons. This longitudinal aspect affects and concerns all data and metadata, from the content itself, to the indices and the statistical metadata maintained for it. Moreover, advanced analysts prefer to deal with semantically rich entities like people, places, organizations, and ideally relationships such as company acquisitions, instead of, say, Web pages containing such references. For example, tracking and analyzing a politician's public appearances over a decade is much harder than mining frequently used query words or frequently clicked URLs for the last month. The huge size of Web archives adds to the complexity of this daunting task. This paper discusses key challenges, that we intend to take up, which are posed by this kind of longitudinal analytics: time-travel indexing and querying, entity detection and tracking along the time axis, algorithms for advanced analyses and knowledge discovery, and scalability and platform issues.