Most time series data mining algorithms use similarity search as a core subroutine, and thus the time taken for similarity search is the bottleneck for virtually all time series data mining algorithms, including classification, clustering, motif discovery, anomaly detection, and so on. The difficulty of scaling a search to large datasets explains to a great extent why most academic work on time series data mining has plateaued at considering a few millions of time series objects, while much of industry and science sits on billions of time series objects waiting to be explored. In this work we show that by using a combination of four novel ideas we can search and mine massive time series for the first time. We demonstrate the following unintuitive fact: in large datasets we can exactly search under Dynamic Time Warping (DTW) much more quickly than the current state-of-the-art <i>Euclidean distance</i> search algorithms. We demonstrate our work on the largest set of time series experiments ever attempted. In particular, the largest dataset we consider is larger than the combined size of all of the time series datasets considered in all data mining papers ever published. We explain how our ideas allow us to solve higher-level time series data mining problems such as motif discovery and clustering at scales that would otherwise be untenable. Moreover, we show how our ideas allow us to efficiently support the uniform scaling distance measure, a measure whose utility seems to be underappreciated, but which we demonstrate here. In addition to mining massive datasets with up to one trillion datapoints, we will show that our ideas also have implications for real-time monitoring of data streams, allowing us to handle much faster arrival rates and/or use cheaper and lower powered devices than are currently possible.