Since its discovery almost 200 years ago, least squares has been the most popular method of regression analysis. A statistics book with the word "regression" in its title, without any qualifying adjective such as "robust" or "nonparametric" or "alternative", can be assumed to be about least-squares regression. Over the last two or three decades, however, there has been increasing interest in other methods. This is due partly to discoveries of deficiencies in the least-squares method and partly to advances in computer technology, which have made the computational complexity of other methods a relatively unimportant consideration. Numerous research articles have now been published on alternative approaches to regression analysis.
Development of these approaches continues and it is likely that further research and experience will lead to modifications and improvements. But enough knowledge and experience have already been accumulated to be able to say that currently proposed alternative methods give reasonable results, have worthwhile advantages over least-squares methods, and can be recommended for practical use.