Originally from Statistical Odds and Ends, there is a nicely brief summary of the Tukey Loss Function. 

I’d love to see what this does in various kinds of regression. It may be possible to set up some kind of iterative regression scheme, where a normal regression with uniform weights is first done, and then the residuals are used to define a set of alternative weights via the Tukey Loss Function. Then the weighted regression is done, producing another set of residuals, and a new set of weights is defined. This should (eventually) settle down.

Here’s the article: