Many time series data mining problems require subsequence similarity search as a subroutine. Dozens of similarity/distance measures have been proposed in the last decade and there is increasing evidence that Dynamic Time Warping (DTW) is the best measure across a wide range of domains. Given DTW's usefulness and ubiquity, there has been a large community-wide effort to mitigate its relative lethargy. Proposed speedup techniques include early abandoning strategies, lower-bound based pruning, indexing and embedding. In this work we argue that we are now close to exhausting all possible speedup from software, and that we must turn to hardware-based solutions. With this motivation, we investigate both GPU (Graphics Processing Unit) and FPGA (Field Programmable Gate Array) based acceleration of subsequence similarity search under the DTW measure. As we shall show, our novel algorithms allow GPUs to achieve two orders of magnitude speedup and FPGAs to produce four orders of magnitude speedup. We conduct detailed case studies on the classification of astronomical observations and demonstrate that our ideas allow us to tackle problems that would be untenable otherwise.