The Video Browser Showdown addresses difficult video search challenges through an annual interactive evaluation campaign attracting research teams focusing on interactive video retrieval. The campaign aims to provide insights into the performance of participating interactive video retrieval systems, tested by selected search tasks on large video collections. For the first time in its ten year history, the Video Browser Showdown 2021 was organized in a fully remote setting and hosted a record number of sixteen scoring systems. In this paper, we describe the competition setting, tasks and results and give an overview of state-of-the-art methods used by the competing systems. By looking at query result logs provided by ten systems, we analyze differences in retrieval model performances and browsing times before a correct submission. Through advances in data gathering methodology and tools, we provide a comprehensive analysis of ad-hoc video search tasks, discuss results, task design and methodological challenges. We highlight that almost all top performing systems utilize some sort of joint embedding for text-image retrieval and enable specification of temporal context in queries for known-item search. Whereas a combination of these techniques drive the currently top performing systems, we identify several future challenges for interactive video search engines and the Video Browser Showdown competition itself.