Machine learning has played an important role in the analysis of high-energy physics data for decades. The emergence of deep learning in 2012 allowed for machine learning tools which could adeptly handle higher-dimensional and more complex problems than previously feasible. This review is aimed at the reader who is familiar with high-energy physics but not machine learning. The connections between machine learning and high-energy physics data analysis are explored, followed by an introduction to the core concepts of neural networks, examples of the key results demonstrating the power of deep learning for analysis of LHC data, and discussion of future prospects and concerns.