Indices for climate variability and extremes have been used for a long time, often by assessing days with temperature or precipitation observations above or below specific physically-based thresholds. While these indices provided insight into local conditions, few physically based thresholds have relevance in all parts of the world. Therefore, indices of extremes evolved over time and now often focus on relative thresholds that describe features in the tails of the distributions of meteorological variables. In order to help understand how extremes are changing globally, a subset of the wide range of possible indices is now being coordinated internationally which allows the results of studies from different parts of the world to fit together seamlessly. This paper reviews these as well as other indices of extremes and documents the obstacles to robustly calculating and analyzing indices and the methods developed to overcome these obstacles. Gridding indices are necessary in order to compare observations with climate model output. However, gridding indices from daily data are not always straightforward because averaging daily information from many stations tends to dampen gridded extremes. The paper describes recent progress in attribution of the changes in gridded indices of extremes that demonstrates human influence on the probability of extremes. The paper also describes model projections of the future and wraps up with a discussion of ongoing efforts to refine indices of extremes as they are being readied to contribute to the IPCC's Fifth Assessment Report.