The rapid development of diagnostic technologies in healthcare is leading to higher requirements for physicians to handle and integrate the heterogeneous, yet complementary data that are produced during routine practice. For instance, the personalized diagnosis and treatment planning for a single cancer patient relies on various images (e.g. radiology, pathology and camera images) and non-image data (e.g. clinical data and genomic data). However, such decision-making procedures can be subjective, qualitative, and have large inter-subject variabilities. With the recent advances in multimodal deep learning technologies, an increasingly large number of efforts have been devoted to a key question: how do we extract and aggregate multimodal information to ultimately provide more objective, quantitative computer-aided clinical decision making? This paper reviews the recent studies on dealing with such a question. Briefly, this review will include the (a) overview of current multimodal learning workflows, (b) summarization of multimodal fusion methods, (c) discussion of the performance, (d) applications in disease diagnosis and prognosis, and (e) challenges and future directions.