Respiratory diseases are among the most common causes of severe illness and death worldwide. Prevention and early diagnosis are essential to limit or even reverse the trend that characterizes the diffusion of such diseases. In this regard, the development of advanced computational tools for the analysis of respiratory auscultation sounds can become a game changer for detecting disease-related anomalies, or diseases themselves. In this work, we propose a novel learning framework for respiratory auscultation sound data. Our approach combines state-of-the-art feature extraction techniques and advanced deep-neural-network architectures. Remarkably, to the best of our knowledge, we are the first to model a recurrent-neural-network based learning framework to support the clinician in detecting respiratory diseases, at either level of abnormal sounds or pathology classes. Results obtained on the ICBHI benchmark dataset show that our approach outperforms competing methods on both anomaly-driven and pathology-driven prediction tasks, thus advancing the state-of-the-art in respiratory disease analysis.