The prediction of the cancer cell lines sensitivity to a specific treatment is one of the current challenges in precision medicine. With omics and pharmacogenomics data being available for over 1000 cancer cell lines, several machine learning and deep learning algorithms have been proposed for drug sensitivity prediction. However, deciding which omics data to use and which computational methods can efficiently incorporate data from different sources is the challenge which several research groups are working on. In this review, we summarize recent advances in the representative computational methods that have been developed in the last 2 years on three public datasets: COSMIC, CCLE, NCI-60. These methods aim to improve the prediction of the cancer cell lines sensitivity to a given treatment by incorporating drug's chemical information in the input or using a priori feature selection. Finally, we discuss the latest published method which aims to improve the prediction of clinical drug response of real patients starting from cancer cell line molecular profiles