There is an increasingly pressing need, by several applications in diverse domains, for developing techniques able to index and mine very large collections of sequences, or data series. Examples of such applications come from social media analytics and internet service providers, as well as from a multitude of scientific domains. It is not unusual for these applications to involve numbers of data series in the order of hundreds of millions to billions, which are often times not analyzed in their full detail due to their sheer size.  In this talk, we describe recent efforts in designing techniques for indexing and mining truly massive collections of data series that will enable scientists to easily analyze their data. We show that the main bottleneck in mining such massive datasets is the time taken to build the index, and we thus introduce solutions to this problem. Furthermore, we discuss novel techniques that adaptively create data series indexes, allowing users to correctly answer queries before the indexing task is finished. We also show how our methods allow mining on datasets that would otherwise be completely untenable, including the first published experiments using one billion data series.  Finally, we present our vision for the future in big sequence management research, including the promising directions in terms of distributed processing.