Cancer patients often respond very differently to any given drug. Some patients respond very well, while others do not respond at all, leaving the cancer to grow unimpeded. If we have a good understanding of how this variability in response arises, we will be better able to choose the optimal treatment strategy for each patient. The variability in drug response observed in patients is also seen in cancer cell lines when they are cultured in vitro. Detailed cell-biological studies have revealed many different mechanisms which affect the response of cancer cells to anticancer drugs. Certain mutations can render cells sensitive to a certain drug, while other mutations, or changes in gene expression, can cause resistance. However, since any combination of these drug sensitivity mechanisms can be operating in a particular cell line, it is difficult to predict whether it will be sensitive or resistant to a particular drug. Computational modeling can be used to better understand this complexity. In this dissertation, we developed a novel method, which we call Inference of Signaling Activity, that can be used to infer the contributions of different drug sensitivity- and resistance mechanisms. We used the available knowledge of signal transduction in cells, and integrated multiple data types including mutations, gene amplifications and deletions, gene expression levels, protein phosphorylation, growth rates and drug response data to infer the signaling activities in each cell line. After an extensive characterization of thirty different breast cancer cell lines, we developed a model that can explain a large part of the variability in the response of these cell lines to seven different kinase inhibitors. At the same time, the response of some cell lines was not recapitulated exactly. Using further data-driven analysis, we found a novel determinant of mTOR inhibitor sensitivity. Overexpression of 4EBP1 in breast cancer cells renders them more sensitive to these inhibitors. This modeling approach can now be further developed to determine whether it can also be used to explain and predict the response of cancer patients. Initially this modeling framework did not permit the inclusion of feedback signaling mechanisms, even though we know feedback control to be an important feature of cellular signaling networks. We therefore subsequently extended our framework such that feedback could be included, and with this extension we were able to delineate signaling activities in regulatory networks with multiple, interrelated feedback loops, again taking into account different datasets. An important consideration in this dissertation was the quantification of uncertainty in model parameters, for which we used Bayesian statistics. If the uncertainty in parameter estimates is not taken into account, we can be lulled into a false sense of security and misinterpret which elements of the model are important. We developed a software package with efficient, multi-threaded implementations of various Monte Carlo sampling algorithms, which allowed the inference to be done in workable amounts of time. We further showed in a different biological system – cell cycle regulation in yeast – that the integration of different types of measurements can increase the identifiability of parameters. Finally, we investigated whether Bayesian inference with multiple datasets can be done sequentially using intermediate posterior approximations. Each of these contributions to Bayesian inference with multiple datasets may be used more broadly in modeling different biological systems. Although further development and validation of the drug response models is needed, the use of integrative computational modeling appears to be a promising approach for enabling precision medicine for cancer patients in the future.