\indent This talk will introduce a new class of models which can lead to efficient estimation in multivariate analysis. Some members in the class include the basic envelope model, partial envelope model, inner envelope model, scaled envelope model, and heteroscedastic envelope model. They have the common word ``envelope'' in their names because they are all constructed by enveloping: use reducing subspaces to connect the mean function and the covariance function, so that the number of parameters can be reduced. The application of enveloping is very broad and can be used in many contexts to control parameterization. Theoretical results, simulations and a large number of data examples show that the efficiency gains obtained by enveloping can be substantial.