The wealth of digital information available in our time has become indispensable for a rich variety of tasks. We use data on the Web for work, leisure, and research, aided by various search systems, allowing us to find small needles in giant haystacks. Despite recent advances in personalization and contextualization, however, various types of tasks, ranging from simple lookup tasks to complex, exploratory and analytical ventures, are mainly supported in elementary, "onesize-fits-all" search interfaces.Web archives, keepers of our future cultural heritage, have gathered petabytes of valuable Web data, which characterize our times for future generations. Access to these archives, however, is surprisingly limited: online Web archives usually provide a URL-based Wayback Machine interface, sometimes extended with rudimentary search options. As a result of limited access, Web archives have not been widely used for research so far. For emerging research using Web archives, there is a need to move beyond URL-based and simple search access, towards providing support for complex (re)search tasks.In my thesis, I am exploring ways to move beyond the "one-size-fits-all" approach for search systems, and I work on systems which can support the flow of complex search, also in the context of archived Web data. Rich models of search and research can be incorporated into adaptive search systems, supporting search strategies in various stages of complex search tasks. Concretely, I look at the use case of the Humanities researcher, for which the large, Terabytescale Web archives can be a valuable addition to existing sources utilized to perform research.