In this contribution, we will discuss the opportunities and challenges arising from memory institutions' need to redefine their archival strategies for contemporary collecting in a world of big data. We will reflect on this topic by critically examining the case study of the UK Web Archive, which is made up of the six UK Legal Deposit Libraries: the British Library, National Library of Scotland, National Library of Wales, Bodleian Libraries Oxford, Cambridge University Library and Trinity College Dublin. The UK Web (...) Archive aims to archive, preserve and give access to the UK web space. This is achieved through an annual domain crawl, first undertaken in 2013, in addition to more frequent crawls of key websites and specially curated collections which date back as far as 2005. These collections reflect important aspects of British culture and events that shape society. This commentary will explore a number of questions including: what heritage is captured and what heritage is instead neglected by the UK Web archive? What heritage is created in the form of new data and what are its properties? What are the ethical issues that memory institutions face when developing these web archiving practices? What transformations are required to overcome such challenges and what institutional futures can we envisage? (shrink)