Recent years have witnessed the flourishing of podcasts, a unique type of audio medium. Prior work on podcast content modeling focused on analyzing Automatic Speech Recognition outputs, which ignored vocal, musical, and conversational properties (e.g., energy, humor, and creativity) that uniquely characterize this medium. In this paper, we present an Adversarial Learning-based Podcast Representation (ALPR) that captures non-textual aspects of podcasts. Through extensive experiments on a large-scale podcast dataset (88,728 episodes from 18,433 channels), we show that (1) ALPR significantly outperforms the state-of-the-art features developed for music and speech in predicting the seriousness and energy of podcasts, and (2) incorporating ALPR significantly improves the performance of topic-based podcast-popularity prediction. Our experiments also reveal factors that correlate with podcast popularity.