We explore dynamic evaluation, where sequence models are adapted to the recent sequence history using gradient descent, assigning higher probabilities to re-occurring sequential patterns. We develop a dynamic evaluation approach that outperforms existing adaptation approaches in our comparisons. We apply dynamic evaluation to outperform all previous word-level perplexities on the Penn Treebank and WikiText-2 datasets (achieving 51.1 and 44.3 respectively) and all previous character-level cross-entropies on the text8 and Hutter Prize datasets (achieving 1.19 bits/char and 1.08 bits/char respectively).