This paper reviews methods that have been used to statistically measure the effect of climate on economic value, using historic data on weather, climate, economic activity and other variables. This has been an active area of research for several decades, with many recent developments and discussion of the best way of measuring climate damages. The paper begins with a conceptual framework covering issues relevant to estimating the costs of climate change impacts. It then considers several approaches to econometrically estimate impacts that have been proposed in the literature: cross-sections, linear and non-linear panel methods, long-differences, and partitioning variation. For each method we describe the kind of impacts (short-run vs long-run) estimated, the type of weather or climate variation used, and the pros and cons of the approach.