Cancer is a highly heterogeneous disease with complex underlying biology. For these reasons, effective cancer treatment is still a challenge. Nowadays, it is clear that a cancer therapy that fits all the cases cannot be found, and as a result the design of therapies tailored to the patient's molecular characteristics is needed. Pharmacogenomics aims to study the relationship between an individual's genotype and drug response. Scientists use different biological models, ranging from cell lines to mouse models, as proxies for patients for preclinical and translational studies. The rapid development of "-omics" technologies is increasing the amount of features that can be measured in these models, expanding the possibilities of finding predictive biomarkers of drug response. Finding these relationships requires diverse computational approaches ranging from machine learning to dynamic modeling. Despite major advances, we are still far from being able to precisely predict drug efficacy in cancer models, let alone directly on patients. We believe that the new experimental techniques and computational approaches covered in this review will bring us closer to this goal.