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Predicting disease status for a complex human disease using genomic data is an important, yet challenging, step in personalized medicine. Among many challenges, the so-called curse of dimensionality problem results in unsatisfied performances of many state-of-art machine learning algorithms. A major recent advance in machine learning is the rapid development of deep learning algorithms that can efficiently extract meaningful features from high-dimensional and complex datasets through a stacked and hierarchical learning process. Deep learning has shown breakthrough performance in several areas including image recognition, natural language processing, and speech recognition. However, the performance of deep learning in predicting disease status using genomic datasets is still not well studied. In this article, we performed a review on the four relevant articles that we found through our thorough literature review. All four articles used auto-encoders to project high-dimensional genomic data to a low dimensional space and then applied the state-of-the-art machine learning algorithms to predict disease status based on the low-dimensional representations. This deep learning approach outperformed existing prediction approaches, such as prediction based on probe-wise screening and prediction based on principal component analysis. The limitations of the current deep learning approach and possible improvements were also discussed.