We explore whether we can observe Time's Arrow in a temporal sequence -- is it possible to tell whether a video is running forwards or backwards? We investigate this somewhat philosophical question using computer vision and machine learning techniques. We explore three methods by which we might detect Time's Arrow in video sequences, based on distinct ways in which motion in video sequences might be asymmetric in time. We demonstrate good video forwards/backwards classification results on a selection of YouTube video clips, and on natively-captured sequences (with no temporally-dependent video compression), and examine what motions the models have learned that help discriminate forwards from backwards time.