As the Internet is playing an increasingly central role in our lives, current and future researchers depend on the web to understand our times. The ephemerality of web content has lead to an increasing number of initiatives to collect this content in web archives. The abundance of information available in web archives is essential for researchers in different disciplines, but these archives have hardly been used for research thus far. Several factors influence the non-use of web archives, including limitations in data quantity and legal access. In this paper, we focus on inherent limitations of the bridge between web archive and user: the access interfaces. Initially, web archives only provided URL-based access, necessitating prior knowledge of URL and timeframe of studied web phenomena. To overcome these limitations, various web archives now enriched their functionality with full-text search, facilitating a whole new range of research opportunities, but also introducing new methodological and theoretical challenges (Ben-David and Huurdeman, 2014). Moreover, traditional search systems do not necessarily support the rich interaction needed to facilitate task-sharing between scholar and system. In this paper, we employ a bottom-up approach and review how scholars use web data to define their corpus, to perform analysis and how they disseminate their findings. Based on this literature review, we reveal limitations of current search systems for web archives. Finally, we offer a tentative outlook on more fluid approaches to overcome these limitations, moving from relatively shallow search engines to a broader research engines , potentially supporting the whole research task.