The article discusses how least absolute values (L1) estimators are good at handling outliers and heavy-tailed data, making them useful in data analysis. Efficient algorithms have been developed for L1 estimation in linear models. While L1 estimators are not always unique, they share certain properties. The set of all L1 estimators for a model and data set can be described as a collection of extreme estimators. The properties of these extreme estimators and the L1-estimate set are explored.