Response variable selection arises naturally in many applications, but has not been studied as thoroughly as predictor variable selection. In this talk, I will firstly introduce the envelope model which allows efficient estimation in multivariate linear regression. Then I will discuss response variable selection in both the standard multivariate linear regression and the envelope contexts. Finally I will introduce the sparse envelope model we proposed to perform variable selection on the responses and preserve the efficiency gains offered by the envelope model. We establish consistency and the oracle property and obtain the asymptotic distribution of the sparse envelope estimator.