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Cancer is a leading cause of death worldwide. Identifying the best treatment using computational models to personalize drug response prediction holds great promise to improve patient’s chances of successful recovery. Unfortunately, the computational task of predicting drug response is very challenging, partially due to the limitations of the available data and partially due to algorithmic shortcomings. The recent advances in deep learning may open a new chapter in the search for computational drug response prediction models and ultimately result in more accurate tools for therapy response. This review provides an overview of the computational challenges and advances in drug response prediction, and focuses on comparing the machine learning techniques to be of utmost practical use for clinicians and machine learning non-experts. The incorporation of new data modalities such as single-cell profiling, along with techniques that rapidly find effective drug combinations will likely be instrumental in improving cancer care.