The discipline of Deep Learning has been recognized for its strong computational tools, which have been extensively used in data and signal processing, with innumerable promising results. Among the many commercial applications of Deep Learning, Music Signal Processing has received an increasing amount of attention over the last decade. This work reviews the most recent developments in Deep Learning in Music signal processing. Two main applications that are discussed are Music Information Retrieval, which spans a plethora of applications, and Music Generation, which can fit a range of musical styles. After a review of both topics, several emerging directions are identified for future research.