Despite the availability of extensive data sets, it is often impractical to observe the responses or labels for all data points due to various measurement constraints in many applications. To address this challenge, subsampling approaches can be employed to select a subset of design points from a large pool for observation, resulting in substantial savings in labeling costs. In this presentation, I will introduce our recent research on computationally feasible subsampling techniques. Our primary focus is on regression with labeled data, which includes linear regression, ridge regression, and nonparametric additive regression. For these regression tasks, we have developed sampling probabilities that aim to minimize the mean squared error in estimations and predictions. We will demonstrate the effectiveness of our proposed approaches through both theoretical analysis and extensive simulations.