Image regression is an important problem in computer vision and is useful in a variety of applications. However, training a robust regression model necessitates large amounts of labeled training data, which is time-consuming and expensive to acquire. Active learning algorithms automatically identify the salient and exemplar instances from large amounts of unlabeled data and tremendously reduce human annotation effort in inducing a machine learning model. Further, deep learning models like Convolutional Neural Networks (CNNs) have gained popularity to automatically learn representative features from a given dataset and have depicted promising performance in a variety of classification and regression applications. In this chapter, we exploit the feature learning capabilities of deep neural networks and propose a novel framework to address the problem of active learning for regression. We formulate a loss function (based on the expected model output change) relevant to the research task and exploit the gradient descent algorithm to optimize the loss and train the deep CNN. To the best of our knowledge, this is the first research effort to learn a discriminative set of features using deep neural networks to actively select informative samples in the regression setting. Our extensive empirical studies on five benchmark regression datasets (from three different application domains: rotation angle estimation of handwritten digits, age, and head pose estimation) demonstrate the merit of our framework in tremendously reducing human annotation effort to induce a robust regression model.