As a general approach on statistical data analysis, asymptotic theory of M-estimation in regression model has received extensive attention. In this talk, we briefly survey some contributions to asymptotic theory on M-estimation in linear models, including the weak and strong consistency, asymptotic normality and the Bahadur representation of M-estimates of the regression coefficients. As a special case, the least absolute deviations estimation plays an important role and is of special interest, and we will pay much attention to them as well.