We review some recent developments on the calculation of the Gini concentration index when data are incomplete, and in particular left- or right- censored or truncated. The right censored case is most common when dealing with survival data, while the other cases are more typical of income or wealth data. For parametric settings, the index can be estimated together with a confidence interval. In nonparametric settings, a restricted version of the Gini index has been defined, or nonparametric bounds for the index can be constructed. Both R and Stata software is now available to implement the methods.